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In
physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fun ...
, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential
expansion of space The expansion of the universe is the increase in distance Distance is a numerical measurement Measurement is the quantification (science), quantification of variable and attribute (research), attributes of an object or event, which can be ...
in the early
universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxy, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development ...

universe
. The
inflationary epoch __NOTOC__ In physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of th ...
lasted from  seconds after the conjectured
Big Bang The Big Bang theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously making sense of things, applying logic ...

Big Bang
singularity to some time between and  seconds after the singularity. Following the inflationary period, the universe continued to expand, but at a slower rate. The acceleration of this expansion due to
dark energy In physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the unive ...

dark energy
began after the universe was already over 7.7 billion years old (5.4 billion years ago). Inflation theory was developed in the late 1970s and early 80s, with notable contributions by several
theoretical physicists The following is a partial list of notable theoretical physicists. Arranged by century of birth, then century of death, then year of birth. For explanation of symbols, see Notes at end of this article. Ancient times * Thales (c. 624 – c. 546 BCE ...
, including
Alexei Starobinsky Alexei Alexandrovich Starobinsky (russian: Алексе́й Алекса́ндрович Староби́нский; born 19 April 1948) is a Soviet Union, Soviet and Russian astrophysicist and cosmologist. He received the Kavli Prize in Astrophy ...

Alexei Starobinsky
at
Landau Institute for Theoretical Physics The L. D. Landau Institute for Theoretical Physics of the Russian Academy of Sciences is a research institution, located in the small town of Chernogolovka near Moscow (there is also a subdivision in Moscow, on the territory of the Institute for P ...

Landau Institute for Theoretical Physics
,
Alan Guth Alan Harvey Guth (; born February 27, 1947) is an American theoretical physicist and cosmologist. Guth has researched elementary particle theory (and how particle theory is applicable to the early universe). He is Victor Weisskopf Professor of ...
at
Cornell University Cornell University is a private Private or privates may refer to: Music * "In Private "In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an absence of nearly two ...
, and
Andrei Linde Andrei Dmitriyevich Linde (russian: Андре́й Дми́триевич Ли́нде; born March 2, 1948) is a Russian-American theoretical A theory is a rational Rationality is the quality or state of being rational – that is, being b ...

Andrei Linde
at
Lebedev Physical Institute The Lebedev Physical Institute of the Russian Academy of Sciences (LPI RAS or just LPI) (in russian: Физи́ческий институ́т имени П.Н.Ле́бедева Российской академии наук (ФИАН)), situated ...
. Alexei Starobinsky, Alan Guth, and Andrei Linde won the 2014
Kavli Prize The Kavli Prize was established in 2005 through a joint venture between the Norwegian Academy of Science and Letters The Norwegian Academy of Science and Letters ( no, Det Norske Videnskaps-Akademi, DNVA) is a learned society A learned soc ...
"for pioneering the theory of cosmic inflation." It was developed further in the early 1980s. It explains the origin of the
large-scale structure of the cosmos The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time, because the electromagnetic radiation from these ...
.
Quantum fluctuation In quantum physics Quantum mechanics is a fundamental theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously m ...
s in the microscopic inflationary region, magnified to cosmic size, become the seeds for the growth of structure in the Universe (see
galaxy formation and evolution The study of galaxy formation and evolution is concerned with the processes that formed a heterogeneous Homogeneity and heterogeneity are concepts often used in the sciences Science (from the Latin Latin (, or , ) is a classical lan ...
and
structure formation In physical cosmology, structure formation is the formation of galaxies, galaxy clusters and larger structures from small early density fluctuations. The universe, as is now known from observations of the cosmic microwave background radiation, b ...
). Many physicists also believe that inflation explains why the universe appears to be the same in all directions (
isotropic Isotropy is uniformity in all orientations; it is derived from the Greek ''isos'' (ἴσος, "equal") and ''tropos'' (τρόπος, "way"). Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by ...
), why the
cosmic microwave background The cosmic microwave background (CMB, CMBR), in Big Bang The Big Bang theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity ...
radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and f ...

radiation
is distributed evenly, why the universe is
flat Flat or flats may refer to: Architecture * Flat (housing), an apartment in the United Kingdom, Ireland, Australia and other Commonwealth countries Arts and entertainment * Flat (music), a symbol () which denotes a lower pitch * Flat (soldier), a ...
, and why no
magnetic monopole In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that departmen ...
s have been observed. The detailed
particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which rel ...
mechanism responsible for inflation is unknown. The basic inflationary paradigm is accepted by most physicists, as a number of inflation model predictions have been confirmed by observation; however, a substantial minority of scientists dissent from this position. The hypothetical
field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grassl ...
thought to be responsible for inflation is called the
inflaton The inflaton field is a hypothetical scalar field In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), an ...
. In 2002 three of the original architects of the theory were recognized for their major contributions; physicists
Alan Guth Alan Harvey Guth (; born February 27, 1947) is an American theoretical physicist and cosmologist. Guth has researched elementary particle theory (and how particle theory is applicable to the early universe). He is Victor Weisskopf Professor of ...
of
M.I.T. Massachusetts Institute of Technology (MIT) is a in . Established in 1861, MIT has since played a key role in the development of modern technology and science, ranking it among the top in the world. Founded in response to the increasing ...
,
Andrei Linde Andrei Dmitriyevich Linde (russian: Андре́й Дми́триевич Ли́нде; born March 2, 1948) is a Russian-American theoretical A theory is a rational Rationality is the quality or state of being rational – that is, being b ...

Andrei Linde
of
Stanford Stanford University, officially Leland Stanford Junior University, is a Private university, private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Sta ...

Stanford
, and
Paul Steinhardt Paul Joseph Steinhardt (born December 25, 1952) is an American theoretical physicist Theoretical physics is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Phys ...
of
Princeton Princeton University is a private Private or privates may refer to: Music * "In Private "In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an absence of nearly tw ...

Princeton
shared the prestigious
Dirac Prize The Dirac Medal is the name of four award An award, sometimes called a distinction, is something given to a recipient as a token of recognition of excellence in a certain field. When the token is a medal, ribbon or other item designed for weari ...
"for development of the concept of inflation in cosmology". In 2012 Guth and Linde were awarded the
Breakthrough Prize in Fundamental Physics The Breakthrough Prize The Breakthrough Prizes are a set of international awards bestowed in three categories by the Breakthrough Prize Board in recognition of scientific advances. The awards are part of several "Breakthrough" initiatives foun ...
for their invention and development of inflationary cosmology.


Overview

Around 1930,
Edwin Hubble Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an American astronomer. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology. Hubble proved that many objects previously ...
discovered that light from remote galaxies was
redshift In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

redshift
ed; the more remote, the more shifted. This was quickly interpreted as meaning galaxies were receding from Earth. If Earth is not in some special, privileged, central position in the universe, then it would mean all galaxies are moving apart, and the further away, the faster they are moving away. It is now understood that the universe is expanding, carrying the galaxies with it, and causing this observation. Many other observations agree, and also lead to the same conclusion. However, for many years it was not clear why or how the universe might be expanding, or what it might signify. Based on a huge amount of experimental observation and theoretical work, it is now believed that the reason for the observation is that ''space itself is expanding'', and that it expanded very rapidly within the first fraction of a second after the
Big Bang The Big Bang theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously making sense of things, applying logic ...

Big Bang
. This kind of expansion is known as a ''"metric"'' expansion. In the terminology of mathematics and physics, a "
metric Metric or metrical may refer to: * Metric system, an internationally adopted decimal system of measurement Mathematics * Metric (mathematics), an abstraction of the notion of ''distance'' in a metric space * Metric tensor, in differential geomet ...
" is a measure of distance that satisfies a specific list of properties, and the term implies that ''the sense of distance within the universe is itself changing''. Today, metric variation is far too small an effect to see on less than an intergalactic scale. The modern explanation for the metric expansion of space was proposed by physicist
Alan Guth Alan Harvey Guth (; born February 27, 1947) is an American theoretical physicist and cosmologist. Guth has researched elementary particle theory (and how particle theory is applicable to the early universe). He is Victor Weisskopf Professor of ...
in 1979, while investigating the problem of why no
magnetic monopoles In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that departmen ...
are seen today. He found that if the universe contained a
field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the infrastructure of an airport * Battlefield * Lawn, an area of mowed grass * Meadow, a grassl ...
in a positive-energy
false vacuum In quantum field theory In theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, na ...
state, then according to
general relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
it would generate an exponential expansion of space. It was very quickly realized that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look like it does ''today'', the Universe would have to have started from very finely tuned, or "special" initial conditions at the Big Bang. Inflation theory largely resolves these problems as well, thus making a universe like ours much more likely in the context of Big Bang theory. No physical field has yet been discovered that is responsible for this inflation. However such a field would be
scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers *Scalar (physics), a physical quantity that can be described by a single element of a number field such as ...

scalar
and the first relativistic scalar field proven to exist, the
Higgs field The Higgs boson is an elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include the fundam ...
, was only discovered in 2012–2013 and is still being researched. So it is not seen as problematic that a field responsible for cosmic inflation and the metric expansion of space has not yet been discovered. The proposed field and its (the
subatomic particle In physical sciences, subatomic particles are smaller than atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All ...
s related to it) have been named the
inflaton The inflaton field is a hypothetical scalar field In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), an ...
. If this field did not exist, scientists would have to propose a different explanation for all the observations that strongly suggest a metric expansion of space has occurred, and is still occurring (much more slowly) today.


Theory

An expanding universe generally has a
cosmological horizon A cosmological horizon is a measure of the distance from which one could possibly retrieve information. This observable constraint is due to various properties of general relativity General relativity, also known as the general theory of rela ...
, which, by analogy with the more familiar
horizon The horizon is the apparent line that separates the surface of a celestial body In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that st ...

horizon
caused by the curvature of
Earth Earth is the third planet from the Sun and the only astronomical object known to harbour and support life. 29.2% of Earth's surface is land consisting of continents and islands. The remaining 70.8% is Water distribution on Earth, covered wi ...

Earth
's surface, marks the boundary of the part of the Universe that an observer can see. Light (or other radiation) emitted by objects beyond the cosmological horizon in an
accelerating universe Observations show that the expansion of the universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the p ...
never reaches the observer, because the space in between the observer and the object is expanding too rapidly. The
observable universe The observable universe is a ball-shaped region of the universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxy, galaxies, and all other forms of matter and energy. The Big Bang th ...
is one ''causal patch'' of a much larger unobservable universe; other parts of the Universe cannot communicate with Earth yet. These parts of the Universe are outside our current cosmological horizon. In the standard hot big bang model, without inflation, the cosmological horizon moves out, bringing new regions into view. Yet as a local observer sees such a region for the first time, it looks no different from any other region of space the local observer has already seen: its background radiation is at nearly the same temperature as the background radiation of other regions, and its space-time curvature is evolving lock-step with the others. This presents a mystery: how did these new regions know what temperature and curvature they were supposed to have? They couldn't have learned it by getting signals, because they were not previously in communication with our past
light cone In special and general relativity, a light cone is the path that a flash of light, emanating from a single event Event may refer to: Gatherings of people * Ceremony A ceremony (, ) is a unified ritual A ritual is a sequence of activities ...

light cone
.Using Tiny Particles To Answer Giant Questions
Science Friday, 3 April 2009.
Inflation answers this question by postulating that all the regions come from an earlier era with a big vacuum energy, or cosmological constant. A space with a cosmological constant is qualitatively different: instead of moving outward, the cosmological horizon stays put. For any one observer, the distance to the
cosmological horizon A cosmological horizon is a measure of the distance from which one could possibly retrieve information. This observable constraint is due to various properties of general relativity General relativity, also known as the general theory of rela ...

cosmological horizon
is constant. With exponentially expanding space, two nearby observers are separated very quickly; so much so, that the distance between them quickly exceeds the limits of communications. The spatial slices are expanding very fast to cover huge volumes. Things are constantly moving beyond the cosmological horizon, which is a fixed distance away, and everything becomes homogeneous. As the inflationary field slowly relaxes to the vacuum, the cosmological constant goes to zero and space begins to expand normally. The new regions that come into view during the normal expansion phase are exactly the same regions that were pushed out of the horizon during inflation, and so they are at nearly the same temperature and curvature, because they come from the same originally small patch of space. The theory of inflation thus explains why the temperatures and curvatures of different regions are so nearly equal. It also predicts that the total curvature of a space-slice at constant global time is zero. This prediction implies that the total ordinary matter,
dark matter Dark matter is a hypothetical form of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, ...

dark matter
and residual
vacuum energy Vacuum energy is an underlying background energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to ...
in the Universe have to add up to the critical density, and the evidence supports this. More strikingly, inflation allows physicists to calculate the minute differences in temperature of different regions from quantum fluctuations during the inflationary era, and many of these quantitative predictions have been confirmed.


Space expands

In a space that expands exponentially (or nearly exponentially) with time, any pair of free-floating objects that are initially at rest will move apart from each other at an accelerating rate, at least as long as they are not bound together by any force. From the point of view of one such object, the spacetime is something like an inside-out Schwarzschild black hole—each object is surrounded by a spherical event horizon. Once the other object has fallen through this horizon it can never return, and even light signals it sends will never reach the first object (at least so long as the space continues to expand exponentially). In the approximation that the expansion is exactly exponential, the horizon is static and remains a fixed physical distance away. This patch of an inflating universe can be described by the following
metric Metric or metrical may refer to: * Metric system, an internationally adopted decimal system of measurement Mathematics * Metric (mathematics), an abstraction of the notion of ''distance'' in a metric space * Metric tensor, in differential geomet ...
: : ds^2=- (1- \Lambda r^2) \, dt^2 + \, dr^2 + r^2 \, d\Omega^2. This exponentially expanding spacetime is called a
de Sitter space In mathematical physics, ''n''-dimensional de Sitter space (often abbreviated to dS''n'') is a maximally symmetric Lorentzian manifold with constant positive scalar curvature. It is the Lorentzian analogue of an n-sphere, ''n''-sphere (with i ...
, and to sustain it there must be a cosmological constant, a
vacuum energy Vacuum energy is an underlying background energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to ...

vacuum energy
density that is constant in space and time and proportional to Λ in the above metric. For the case of exactly exponential expansion, the vacuum energy has a negative pressure ''p'' equal in magnitude to its energy density ''ρ''; the
equation of state In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through S ...
is ''p=−ρ''. Inflation is typically not an exactly exponential expansion, but rather quasi- or near-exponential. In such a universe the horizon will slowly grow with time as the vacuum energy density gradually decreases.


Few inhomogeneities remain

Because the accelerating expansion of space stretches out any initial variations in density or temperature to very large length scales, an essential feature of inflation is that it smooths out inhomogeneities and
anisotropies Anisotropy () is the property of a material which allows it to change or assume different properties in different directions as opposed to isotropy Isotropy is uniformity in all orientations; it is derived from the Greek ''isos'' (ἴσος, ...
, and reduces the
curvature of space In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities an ...
. This pushes the Universe into a very simple state in which it is completely dominated by the
inflaton The inflaton field is a hypothetical scalar field In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), an ...
field and the only significant inhomogeneities are tiny
quantum fluctuation In quantum physics Quantum mechanics is a fundamental theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously m ...
s. Inflation also dilutes exotic heavy particles, such as the
magnetic monopole In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that departmen ...
s predicted by many extensions to the
Standard Model The Standard Model of particle physics Particle physics (also known as high energy physics) is a branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsi ...

Standard Model
of
particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which rel ...
. If the Universe was only hot enough to form such particles ''before'' a period of inflation, they would not be observed in nature, as they would be so rare that it is quite likely that there are none in the
observable universe The observable universe is a ball-shaped region of the universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxy, galaxies, and all other forms of matter and energy. The Big Bang th ...
. Together, these effects are called the inflationary "no-hair theorem" by analogy with the
no hair theorem The no-hair theorem states that all black hole solutions of the Einstein–Maxwell equations of gravitation Gravity (), or gravitation, is a natural phenomenon Types of natural phenomena include: Weather, fog, thunder, tornadoes; ...
for s. The "no-hair" theorem works essentially because the cosmological horizon is no different from a black-hole horizon, except for philosophical disagreements about what is on the other side. The interpretation of the no-hair theorem is that the Universe (observable and unobservable) expands by an enormous factor during inflation. In an expanding universe, generally fall, or get diluted, as the volume of the Universe increases. For example, the density of ordinary "cold" matter (dust) goes down as the inverse of the volume: when linear dimensions double, the energy density goes down by a factor of eight; the radiation energy density goes down even more rapidly as the Universe expands since the wavelength of each
photon The photon ( el, φῶς, phōs, light) is a type of elementary particle In , an elementary particle or fundamental particle is a that is not composed of other particles. Particles currently thought to be elementary include the fundamental s ...

photon
is stretched (
redshift In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

redshift
ed), in addition to the photons being dispersed by the expansion. When linear dimensions are doubled, the energy density in radiation falls by a factor of sixteen (see the solution of the energy density continuity equation for an ultra-relativistic fluid). During inflation, the energy density in the inflaton field is roughly constant. However, the energy density in everything else, including inhomogeneities, curvature, anisotropies, exotic particles, and standard-model particles is falling, and through sufficient inflation these all become negligible. This leaves the Universe flat and symmetric, and (apart from the homogeneous inflaton field) mostly empty, at the moment inflation ends and reheating begins.


Duration

A key requirement is that inflation must continue long enough to produce the present observable universe from a single, small inflationary
Hubble volume In cosmology Cosmology (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its pop ...
. This is necessary to ensure that the Universe appears flat, homogeneous and isotropic at the largest observable scales. This requirement is generally thought to be satisfied if the Universe expanded by a factor of at least during inflation.


Reheating

Inflation is a period of supercooled expansion, when the temperature drops by a factor of 100,000 or so. (The exact drop is model-dependent, but in the first models it was typically from  K down to  K.) This relatively low temperature is maintained during the inflationary phase. When inflation ends the temperature returns to the pre-inflationary temperature; this is called ''reheating'' or thermalization because the large potential energy of the inflaton field decays into particles and fills the Universe with
Standard Model The Standard Model of particle physics Particle physics (also known as high energy physics) is a branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsi ...

Standard Model
particles, including
electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...

electromagnetic radiation
, starting the radiation dominated phase of the Universe. Because the nature of the inflation is not known, this process is still poorly understood, although it is believed to take place through a parametric resonance.


Motivations

Inflation resolves several problems in
Big Bang The Big Bang theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously making sense of things, applying logic ...

Big Bang
cosmology that were discovered in the 1970s. Inflation was first proposed by
Alan Guth Alan Harvey Guth (; born February 27, 1947) is an American theoretical physicist and cosmologist. Guth has researched elementary particle theory (and how particle theory is applicable to the early universe). He is Victor Weisskopf Professor of ...
in 1979 while investigating the problem of why no
magnetic monopoles In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that departmen ...
are seen today; he found that a positive-energy
false vacuum In quantum field theory In theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, na ...
would, according to
general relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
, generate an exponential expansion of space. It was very quickly realised that such an expansion would resolve many other long-standing problems. These problems arise from the observation that to look like it does ''today'', the Universe would have to have started from very finely tuned, or "special" initial conditions at the Big Bang. Inflation attempts to resolve these problems by providing a dynamical mechanism that drives the Universe to this special state, thus making a universe like ours much more likely in the context of the Big Bang theory.


Horizon problem

The
horizon problem The horizon problem (also known as the homogeneity problem) is a cosmological Cosmology (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the He ...

horizon problem
is the problem of determining why the Universe appears statistically homogeneous and isotropic in accordance with the
cosmological principle #REDIRECT Cosmological principle In modern physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale ...
. For example, molecules in a canister of gas are distributed homogeneously and isotropically because they are in thermal equilibrium: gas throughout the canister has had enough time to interact to dissipate inhomogeneities and anisotropies. The situation is quite different in the big bang model without inflation, because gravitational expansion does not give the early universe enough time to equilibrate. In a big bang with only the
matter In classical physics Classical physics is a group of physics theories that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major ...
and
radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and f ...

radiation
known in the Standard Model, two widely separated regions of the observable universe cannot have equilibrated because they move apart from each other faster than the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
and thus have never come into causal contact. In the early Universe, it was not possible to send a light signal between the two regions. Because they have had no interaction, it is difficult to explain why they have the same temperature (are thermally equilibrated). Historically, proposed solutions included the ''Phoenix universe'' of
Georges Lemaître Georges Henri Joseph Édouard Lemaître ( ; ; 17 July 1894 – 20 June 1966) was a Belgian Belgian may refer to: * Something of, or related to, Belgium Belgium, ; french: Belgique ; german: Belgien officially the Kingdom of Belgium, is ...
, the related
oscillatory universe A cyclic model (or oscillating model) is any of several cosmological model Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the ...
of
Richard Chase Tolman Richard Chace Tolman (March 4, 1881 – September 5, 1948) was an American mathematical physicist Mathematical physics refers to the development of mathematical Mathematics (from Greek: ) includes the study of such topics as numb ...
, and the
Mixmaster universe The Mixmaster universe (named after Sunbeam Mixmaster, a brand of Sunbeam Products electric kitchen mixer)Barry R. Parker, ''Chaos in the Cosmos: The Stunning Complexity of the Universe'', Springer, 2013, p. 257. is a solution to Einstein field equa ...
of
Charles Misner Charles W. Misner (; born June 13, 1932) is an American physicist and one of the authors of ''Gravitation (book), Gravitation''. His specialties include general relativity and cosmology. His work has also provided early foundations for studies o ...
. Lemaître and Tolman proposed that a universe undergoing a number of cycles of contraction and expansion could come into thermal equilibrium. Their models failed, however, because of the buildup of
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

entropy
over several cycles. Misner made the (ultimately incorrect) conjecture that the Mixmaster mechanism, which made the Universe ''more'' chaotic, could lead to statistical homogeneity and isotropy.


Flatness problem

The
flatness problem The flatness problem (also known as the oldness problem) is a cosmological Cosmology (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellen ...
is sometimes called one of the Dicke coincidences (along with the
cosmological constant problem In cosmology, the cosmological constant problem or vacuum catastrophe is the disagreement between the observed values of vacuum energy energy density, density (the small value of the cosmological constant) and theoretical large value of zero-poi ...
). It became known in the 1960s that the density of matter in the Universe was comparable to the critical density necessary for a flat universe (that is, a universe whose large scale
geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat ...

geometry
is the usual
Euclidean geometry Euclidean geometry is a mathematical system attributed to Alexandria Alexandria ( or ; ar, الإسكندرية ; arz, اسكندرية ; Coptic Coptic may refer to: Afro-Asia * Copts, an ethnoreligious group mainly in the area of modern ...
, rather than a non-Euclidean
hyperbolic Hyperbolic is an adjective describing something that resembles or pertains to a hyperbola (a curve), to hyperbole (an overstatement or exaggeration), or to hyperbolic geometry. The following phenomena are described as ''hyperbolic'' because they ...
or
spherical geometry file:Spherical_triangle_3d.png, 300px, A sphere with a spherical triangle on it. Spherical geometry is the geometry of the two-dimensional surface of a sphere. In this context the word "sphere" refers only to the 2-dimensional surface and othe ...
). Therefore, regardless of the
shape of the universe The shape of the universe, in physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structure ...
the contribution of spatial curvature to the expansion of the Universe could not be much greater than the contribution of matter. But as the Universe expands, the curvature
redshift In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular ...

redshift
s away more slowly than matter and radiation. Extrapolated into the past, this presents a
fine-tuning In theoretical physics, fine-tuning is the process in which parameters of a model must be adjusted very precisely in order to fit with certain observations. This had led to the discovery that the fundamental constants and quantities fall into suc ...
problem because the contribution of curvature to the Universe must be exponentially small (sixteen orders of magnitude less than the density of radiation at
Big Bang nucleosynthesis In physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the univer ...
, for example). This problem is exacerbated by recent observations of the cosmic microwave background that have demonstrated that the Universe is flat to within a few percent.


Magnetic-monopole problem

The magnetic monopole problem, sometimes called the exotic-relics problem, says that if the early universe were very hot, a large number of very heavy, stable
magnetic monopole In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that departmen ...
s would have been produced. This is a problem with
Grand Unified Theories A Grand Unified Theory (GUT) is a model in particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of a ...
, which propose that at high temperatures (such as in the early universe) the
electromagnetic force Electromagnetism is a branch of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related ...
, strong, and weak
nuclear force The nuclear force (or nucleon–nucleon interaction, residual strong force, or, historically, strong nuclear force) is a force that acts between the proton A proton is a subatomic particle, symbol or , with a positive electric charge of +1 ...

nuclear force
s are not actually fundamental forces but arise due to
spontaneous symmetry breaking Spontaneous symmetry breaking is a spontaneous process In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical proper ...

spontaneous symmetry breaking
from a single
gauge theory In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...
. These theories predict a number of heavy, stable particles that have not been observed in nature. The most notorious is the magnetic monopole, a kind of stable, heavy "charge" of magnetic field. Monopoles are predicted to be copiously produced following Grand Unified Theories at high temperature, and they should have persisted to the present day, to such an extent that they would become the primary constituent of the Universe. Not only is that not the case, but all searches for them have failed, placing stringent limits on the density of relic magnetic monopoles in the Universe. A period of inflation that occurs below the temperature where magnetic monopoles can be produced would offer a possible resolution of this problem: monopoles would be separated from each other as the Universe around them expands, potentially lowering their observed density by many orders of magnitude. Though, as cosmologist
Martin Rees Martin John Rees, Baron Rees of Ludlow, One or more of the preceding sentences incorporates text from the royalsociety.org website where: (born 23 June 1942) is a British British may refer to: Peoples, culture, and language * British peo ...
has written, "Skeptics about exotic physics might not be hugely impressed by a theoretical argument to explain the absence of particles that are themselves only hypothetical. Preventive medicine can readily seem 100 percent effective against a disease that doesn't exist!"


History


Precursors

In the early days of
General Relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
,
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theo ...

Albert Einstein
introduced the cosmological constant to allow a static solution, which was a three-dimensional sphere with a uniform density of matter. Later,
Willem de Sitter Willem de Sitter (6 May 1872 – 20 November 1934) was a Dutch mathematician, physicist, and astronomer. Life and work Born in Sneek, de Sitter studied mathematics at the University of Groningen and then joined the Groningen (city), Groninge ...

Willem de Sitter
found a highly symmetric inflating universe, which described a universe with a cosmological constant that is otherwise empty. It was discovered that Einstein's universe is unstable, and that small fluctuations cause it to collapse or turn into a de Sitter universe. In the early 1970s
Zeldovich Yakov Borisovich Zeldovich ( be, Я́каў Бары́савіч Зяльдо́віч, russian: Я́ков Бори́сович Зельдо́вич; 8 March 1914 – 2 December 1987), also known as YaB, was a Soviet people, Soviet theoretical ...
noticed the flatness and horizon problems of Big Bang cosmology; before his work, cosmology was presumed to be symmetrical on purely philosophical grounds. In the Soviet Union, this and other considerations led Belinski and Khalatnikov to analyze the chaotic
BKL singularity A Belinski–Khalatnikov–Lifshitz (BKL) singularity is a model of the dynamic evolution of the universe near the initial gravitational singularity A gravitational singularity, spacetime singularity or simply singularity is a condition i ...
in General Relativity. Misner's
Mixmaster universe The Mixmaster universe (named after Sunbeam Mixmaster, a brand of Sunbeam Products electric kitchen mixer)Barry R. Parker, ''Chaos in the Cosmos: The Stunning Complexity of the Universe'', Springer, 2013, p. 257. is a solution to Einstein field equa ...
attempted to use this chaotic behavior to solve the cosmological problems, with limited success.


False vacuum

In the late 1970s,
Sidney Coleman Sidney Richard Coleman (7 March 1937 – 18 November 2007) was an American theoretical physics, theoretical physicist who studied under Murray Gell-Mann. He is noted for his research in high-energy theoretical physics. Life and work Sidne ...
applied the
instanton An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics Mathematical physics refers to the development of mathematical methods for application to problems in physics. The '' Journal of Mathematical Physic ...

instanton
techniques developed by Alexander Polyakov and collaborators to study the fate of the
false vacuum In quantum field theory In theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, na ...
in
quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
. Like a metastable phase in
statistical mechanics In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and forc ...
—water below the freezing temperature or above the boiling point—a quantum field would need to nucleate a large enough bubble of the new vacuum, the new phase, in order to make a transition. Coleman found the most likely decay pathway for vacuum decay and calculated the inverse lifetime per unit volume. He eventually noted that gravitational effects would be significant, but he did not calculate these effects and did not apply the results to cosmology. The universe could have been spontaneously created from nothing (no
space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameter A parameter (from the Ancient Greek language, Ancient Gre ...

space
,
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...

time
, nor
matter In classical physics Classical physics is a group of physics theories that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major ...
) by
quantum fluctuation In quantum physics Quantum mechanics is a fundamental theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously m ...
s of metastable false vacuum causing an expanding bubble of true vacuum.404.1207Spontaneous creation of the universe from nothing">


Starobinsky inflation

In the Soviet Union,
Alexei Starobinsky Alexei Alexandrovich Starobinsky (russian: Алексе́й Алекса́ндрович Староби́нский; born 19 April 1948) is a Soviet Union, Soviet and Russian astrophysicist and cosmologist. He received the Kavli Prize in Astrophy ...

Alexei Starobinsky
noted that quantum corrections to general relativity should be important for the early universe. These generically lead to curvature-squared corrections to the
Einstein–Hilbert action The Einstein–Hilbert action (also referred to as Relativity priority dispute#Did Hilbert claim priority for parts of General Relativity?, Hilbert action) in general relativity is the action (physics), action that yields the Einstein field equatio ...
and a form of ''f''(''R'') modified gravity. The solution to Einstein's equations in the presence of curvature squared terms, when the curvatures are large, leads to an effective cosmological constant. Therefore, he proposed that the early universe went through an inflationary de Sitter era. This resolved the cosmology problems and led to specific predictions for the corrections to the microwave background radiation, corrections that were then calculated in detail. Starobinsky used the action : S=\frac \int d^4 x \left(R + \frac \right) which corresponds to the potential :\quad V(\phi)=\Lambda^4 \left(1 - e^ \right)^2 in the Einstein frame. This results in the observables: n_s=1 - \frac, \quad \quad r=\frac.


Monopole problem

In 1978, Zeldovich noted the monopole problem, which was an unambiguous quantitative version of the horizon problem, this time in a subfield of particle physics, which led to several speculative attempts to resolve it. In 1980
Alan Guth Alan Harvey Guth (; born February 27, 1947) is an American theoretical physicist and cosmologist. Guth has researched elementary particle theory (and how particle theory is applicable to the early universe). He is Victor Weisskopf Professor of ...
realized that false vacuum decay in the early universe would solve the problem, leading him to propose a scalar-driven inflation. Starobinsky's and Guth's scenarios both predicted an initial de Sitter phase, differing only in mechanistic details.


Early inflationary models

Guth proposed inflation in January 1981 to explain the nonexistence of magnetic monopoles;
SLAC SLAC National Accelerator Laboratory, originally named Stanford Linear Accelerator Center, is a United States Department of Energy The United States Department of Energy (DOE) is a cabinet Cabinet or The Cabinet may refer to: Furnitu ...
seminar, " seconds after the Big Bang", 23 January 1980. see Guth (1997), pg 186
it was Guth who coined the term "inflation".Chapter 17 of Peebles (1993). At the same time, Starobinsky argued that quantum corrections to gravity would replace the initial singularity of the Universe with an exponentially expanding de Sitter phase. In October 1980, Demosthenes Kazanas suggested that exponential expansion could eliminate the
particle horizon The particle horizon (also called the cosmological horizon, the comoving horizon (in Dodelson's text), or the cosmic light horizon) is the maximum distance from which light from Elementary particle, particles could have traveled to the observation, ...
and perhaps solve the horizon problem, while Sato suggested that an exponential expansion could eliminate
domain walls A domain wall is a type of topological soliton that occurs whenever a discrete symmetry is spontaneously broken. Domain walls are also sometimes called kinks in analogy with closely related kink solution of the sine-Gordon model or models with polyn ...
(another kind of exotic relic). In 1981 Einhorn and Sato published a model similar to Guth's and showed that it would resolve the puzzle of the
magnetic monopole In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that departmen ...
abundance in Grand Unified Theories. Like Guth, they concluded that such a model not only required fine tuning of the cosmological constant, but also would likely lead to a much too granular universe, i.e., to large density variations resulting from bubble wall collisions. Guth proposed that as the early universe cooled, it was trapped in a
false vacuum In quantum field theory In theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, na ...
with a high energy density, which is much like a cosmological constant. As the very early universe cooled it was trapped in a
metastable In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's ground state, state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. I ...

metastable
state (it was supercooled), which it could only decay out of through the process of via
quantum tunneling In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
. Bubbles of
true vacuum In quantum field theory, a false vacuum is a hypothetical vacuum state, vacuum that is not actively decaying, but somewhat yet not entirely stable ("metastable"). It may last for a very long time in that state (a property known as metastability) ...
spontaneously form in the sea of false vacuum and rapidly begin expanding at the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
. Guth recognized that this model was problematic because the model did not reheat properly: when the bubbles nucleated, they did not generate any radiation. Radiation could only be generated in collisions between bubble walls. But if inflation lasted long enough to solve the initial conditions problems, collisions between bubbles became exceedingly rare. In any one causal patch it is likely that only one bubble would nucleate.


Slow-roll inflation

The bubble collision problem was solved by
Linde Linde may refer to: Places *Lindes and Ramsberg Mountain District, a former district in Sweden, see Lindesberg Municipality *Lipka, Złotów County, a village in Poland, called Linde before World War II Rivers *Linde (Tollense), a river of Meckle ...

Linde
and independently by Andreas Albrecht and
Paul Steinhardt Paul Joseph Steinhardt (born December 25, 1952) is an American theoretical physicist Theoretical physics is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Phys ...
in a model named ''new inflation'' or ''slow-roll inflation'' (Guth's model then became known as ''old inflation''). In this model, instead of tunneling out of a false vacuum state, inflation occurred by a
scalar field In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...

scalar field
rolling down a potential energy hill. When the field rolls very slowly compared to the expansion of the Universe, inflation occurs. However, when the hill becomes steeper, inflation ends and reheating can occur.


Effects of asymmetries

Eventually, it was shown that new inflation does not produce a perfectly symmetric universe, but that quantum fluctuations in the inflaton are created. These fluctuations form the primordial seeds for all structure created in the later universe. These fluctuations were first calculated by
Viatcheslav Mukhanov Viatcheslav Fyodorovich Mukhanov (russian: Вячесла́в Фёдорович Муха́нов; born October 2, 1956) is a Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a socialist state ...
and G. V. Chibisov in analyzing Starobinsky's similar model. In the context of inflation, they were worked out independently of the work of Mukhanov and Chibisov at the three-week 1982 Nuffield Workshop on the Very Early Universe at
Cambridge University The University of Cambridge is a collegiate university, collegiate research university in Cambridge, Cambridge, United Kingdom. Founded in 1209 and granted a royal charter by Henry III of England, Henry III in 1231, Cambridge is the second-oldest ...
. The fluctuations were calculated by four groups working separately over the course of the workshop:
Stephen Hawking Stephen William Hawking (8 January 1942 – 14 March 2018) was an English theoretical physicist Theoretical physics is a branch of physics Physics is the that studies , its , its and behavior through , and the related enti ...

Stephen Hawking
; Starobinsky; Guth and So-Young Pi; and
BardeenBardeen may refer to: *Charles Russell Bardeen (1871–1935), American anatomist, first dean of the medical school of the University of Wisconsin-Madison *Charles V. Bardeen (1850–1903), American jurist *Charles William Bardeen (1847–1924), Amer ...
, Steinhardt and
Turner Turner may refer to: People and fictional characters *Turner (surname), a common surname, including a list of people and fictional characters with the name *Turner (given name), a list of people with the given name *One who uses a lathe for turnin ...
.


Observational status

Inflation is a mechanism for realizing the
cosmological principle #REDIRECT Cosmological principle In modern physical cosmology Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale ...
, which is the basis of the standard model of physical cosmology: it accounts for the homogeneity and isotropy of the observable universe. In addition, it accounts for the observed flatness and absence of magnetic monopoles. Since Guth's early work, each of these observations has received further confirmation, most impressively by the detailed observations of the
cosmic microwave background The cosmic microwave background (CMB, CMBR), in Big Bang The Big Bang theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity ...
made by the
Planck spacecraft ''Planck'' was a space observatory operated by the European Space Agency (ESA) from 2009 to 2013, which mapped the Anisotropy, anisotropies of the cosmic microwave background (CMB) at microwave and infrared frequencies, with high sensitivity an ...
. This analysis shows that the Universe is flat to within 0.5 percent, and that it is homogeneous and isotropic to one part in 100,000. Inflation predicts that the structures visible in the Universe today formed through the
gravitational collapse Gravitational collapse is the contraction of an astronomical object due to the influence of its own gravity, which tends to draw matter inward toward the centre of mass#Centre of gravity, centre of gravity. Gravitational collapse is a fundamenta ...
of perturbations that were formed as quantum mechanical fluctuations in the inflationary epoch. The detailed form of the spectrum of perturbations, called a nearly-scale-invariant
Gaussian random field A Gaussian random field (GRF) is a random fieldIn physics and mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), ...
is very specific and has only two free parameters. One is the amplitude of the spectrum and the ''
spectral index In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses math ...
'', which measures the slight deviation from scale invariance predicted by inflation (perfect scale invariance corresponds to the idealized de Sitter universe). The other free parameter is the tensor to scalar ratio. The simplest inflation models, those without
fine-tuning In theoretical physics, fine-tuning is the process in which parameters of a model must be adjusted very precisely in order to fit with certain observations. This had led to the discovery that the fundamental constants and quantities fall into suc ...
, predict a
tensor In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...
to scalar ratio near 0.1. Inflation predicts that the observed perturbations should be in
thermal equilibrium Two physical system A physical system is a collection of physical objects. In physics, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment (systems), environment. The enviro ...

thermal equilibrium
with each other (these are called '''' or ''
isentropic In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quan ...
'' perturbations). This structure for the perturbations has been confirmed by the
Planck spacecraft ''Planck'' was a space observatory operated by the European Space Agency (ESA) from 2009 to 2013, which mapped the Anisotropy, anisotropies of the cosmic microwave background (CMB) at microwave and infrared frequencies, with high sensitivity an ...
,
WMAP The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP and Explorer 80), was a NASA The National Aeronautics and Space Administration (NASA; ) is an independent agency A regulatory age ...
spacecraft and other cosmic microwave background (CMB) experiments, and
galaxy survey In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses m ...
s, especially the ongoing
Sloan Digital Sky Survey The Sloan Digital Sky Survey or SDSS is a major multi-spectral imaging and spectroscopic redshift survey using a dedicated 2.5-m wide-angle optical telescope at Apache Point Observatory in New Mexico, United States. The project was named after ...
. These experiments have shown that the one part in 100,000 inhomogeneities observed have exactly the form predicted by theory. There is evidence for a slight deviation from scale invariance. The ''
spectral index In astronomy Astronomy (from el, ἀστρονομία, literally meaning the science that studies the laws of the stars) is a natural science that studies astronomical object, celestial objects and celestial event, phenomena. It uses math ...
'', ''n''s is one for a scale-invariant Harrison–Zel'dovich spectrum. The simplest inflation models predict that ''n''s is between 0.92 and 0.98. This is the range that is possible without
fine-tuning In theoretical physics, fine-tuning is the process in which parameters of a model must be adjusted very precisely in order to fit with certain observations. This had led to the discovery that the fundamental constants and quantities fall into suc ...
of the parameters related to energy. From Planck data it can be inferred that ''n''s=0.968 ± 0.006, and a
tensor In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities a ...
to scalar ratio that is less than 0.11. These are considered an important confirmation of the theory of inflation. Various inflation theories have been proposed that make radically different predictions, but they generally have much more fine tuning than should be necessary. As a physical model, however, inflation is most valuable in that it robustly predicts the initial conditions of the Universe based on only two adjustable parameters: the spectral index (that can only change in a small range) and the amplitude of the perturbations. Except in contrived models, this is true regardless of how inflation is realized in particle physics. Occasionally, effects are observed that appear to contradict the simplest models of inflation. The first-year WMAP data suggested that the spectrum might not be nearly scale-invariant, but might instead have a slight curvature. However, the third-year data revealed that the effect was a statistical anomaly. Another effect remarked upon since the first cosmic microwave background satellite, the
Cosmic Background Explorer The Cosmic Background Explorer (COBE ), also referred to as Explorer 66, was a NASA satellite dedicated to physical cosmology, cosmology, which operated from 1989 to 1993. Its goals were to investigate the Cosmic microwave background, cosmic mi ...
is that the amplitude of the
quadrupole moment A quadrupole or quadrapole is one of a sequence of configurations of things like electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansionA multipole expansion is a mathe ...
of the CMB is unexpectedly low and the other low multipoles appear to be preferentially aligned with the ecliptic plane. Some have claimed that this is a signature of non-Gaussianity and thus contradicts the simplest models of inflation. Others have suggested that the effect may be due to other new physics, foreground contamination, or even
publication bias #REDIRECT publication bias #REDIRECT publication bias#REDIRECT publication bias Publication bias is a type of bias Bias is a disproportionate weight ''in favor of'' or ''against'' an idea or thing, usually in a way that is closed-minded, prej ...
. An experimental program is underway to further test inflation with more precise CMB measurements. In particular, high precision measurements of the so-called "B-modes" of the
polarization Polarization or polarisation may refer to: In the physical sciences *Polarization (waves), the ability of waves to oscillate in more than one direction, in particular polarization of light, responsible for example for the glare-reducing effect of ...

polarization
of the background radiation could provide evidence of the
gravitational radiation Gravitational waves are disturbances in the curvature of spacetime In physics, spacetime is any mathematical model which fuses the three-dimensional space, three dimensions of space and the one dimension of time into a single four-dimensional ...
produced by inflation, and could also show whether the energy scale of inflation predicted by the simplest models (–
GeV GEV may refer to: * ''G.E.V.'' (board game), a tabletop game by Steve Jackson Games * Ashe County Airport, in North Carolina, United States * Gällivare Lapland Airport, in Sweden * Generalized extreme value distribution In probability theory ...
) is correct. In March 2014, the
BICEP2 BICEP (Background Imaging of Cosmic Extragalactic Polarization) and the Keck Array are a series of cosmic microwave background (CMB) List of cosmic microwave background experiments, experiments. They aim to measure the Polarization in astronomy, po ...
team announced B-mode CMB polarization confirming inflation had been demonstrated. The team announced the tensor-to-scalar power ratio r was between 0.15 and 0.27 (rejecting the
null hypothesis In inferential statistics, the null hypothesis (often denoted ''H''0) is that there is no difference between two possibilities. The null hypothesis is that the observed difference is due to chance alone. Using statistical tests it is possible to ...
; r is expected to be 0 in the absence of inflation). However, on 19 June 2014, lowered confidence in confirming the findings was reported; on 19 September 2014, a further reduction in confidence was reported and, on 30 January 2015, even less confidence yet was reported. By 2018, additional data suggested, with 95% confidence, that r is 0.06 or lower: consistent with the null hypothesis, but still also consistent with many remaining models of inflation. Other potentially corroborating measurements are expected from the
Planck spacecraft ''Planck'' was a space observatory operated by the European Space Agency (ESA) from 2009 to 2013, which mapped the Anisotropy, anisotropies of the cosmic microwave background (CMB) at microwave and infrared frequencies, with high sensitivity an ...
, although it is unclear if the signal will be visible, or if contamination from foreground sources will interfere. Other forthcoming measurements, such as those of 21 centimeter radiation (radiation emitted and absorbed from neutral hydrogen before the first stars formed), may measure the power spectrum with even greater resolution than the CMB and galaxy surveys, although it is not known if these measurements will be possible or if interference with
radio sources An astronomical radio source is an object in outer space that emits strong radio waves. Radio emission comes from a wide variety of sources. Such objects are among the most extreme and energetic physical processes in the universe. History In 1932, ...
on Earth and in the galaxy will be too great.


Theoretical status

In Guth's early proposal, it was thought that the
inflaton The inflaton field is a hypothetical scalar field In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), an ...
was the
Higgs field The Higgs boson is an elementary particle In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include the fundam ...
, the field that explains the mass of the elementary particles. It is now believed by some that the inflaton cannot be the Higgs field although the recent discovery of the Higgs boson has increased the number of works considering the Higgs field as inflaton. One problem of this identification is the current tension with experimental data at the
electroweak In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department ...
scale, which is currently under study at the Large Hadron Collider (LHC). Other models of inflation relied on the properties of Grand Unified Theories. Since the simplest models of
grand unification A Grand Unified Theory (GUT) is a model in particle physics in which, at high energy, energies, the three gauge theory, gauge interactions of the Standard Model comprising the electromagnetism, electromagnetic, weak interaction, weak, and strong ...
have failed, it is now thought by many physicists that inflation will be included in a
supersymmetric In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical physics, theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supe ...
theory such as
string theory In physics, string theory is a Mathematical theory, theoretical framework in which the Point particle, point-like particles of particle physics are replaced by Dimension (mathematics and physics), one-dimensional objects called String (physic ...

string theory
or a supersymmetric grand unified theory. At present, while inflation is understood principally by its detailed predictions of the
initial conditions In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving Variable (mathematics), variable at some point in time designated as the initial time (typically denoted '' ...
for the hot early universe, the particle physics is largely ''ad hoc'' modelling. As such, although predictions of inflation have been consistent with the results of observational tests, many open questions remain.


Fine-tuning problem

One of the most severe challenges for inflation arises from the need for fine tuning. In new inflation, the ''slow-roll conditions'' must be satisfied for inflation to occur. The slow-roll conditions say that the inflaton
potential Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (ph ...
must be flat (compared to the large
vacuum energy Vacuum energy is an underlying background energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to ...
) and that the inflaton particles must have a small mass. New inflation requires the Universe to have a scalar field with an especially flat potential and special initial conditions. However, explanations for these fine-tunings have been proposed. For example, classically scale invariant field theories, where scale invariance is broken by quantum effects, provide an explanation of the flatness of inflationary potentials, as long as the theory can be studied through
perturbation theory In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no g ...
.
Linde Linde may refer to: Places *Lindes and Ramsberg Mountain District, a former district in Sweden, see Lindesberg Municipality *Lipka, Złotów County, a village in Poland, called Linde before World War II Rivers *Linde (Tollense), a river of Meckle ...

Linde
proposed a theory known as '' chaotic inflation'' in which he suggested that the conditions for inflation were actually satisfied quite generically. Inflation will occur in virtually that begins in a chaotic, high energy state that has a scalar field with unbounded potential energy. However, in his model the inflaton field necessarily takes values larger than one Planck unit: for this reason, these are often called ''large field'' models and the competing new inflation models are called ''small field'' models. In this situation, the predictions of
effective field theory In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
are thought to be invalid, as
renormalization Renormalization is a collection of techniques in quantum field theory In theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, expl ...
should cause large corrections that could prevent inflation. This problem has not yet been resolved and some cosmologists argue that the small field models, in which inflation can occur at a much lower energy scale, are better models. While inflation depends on quantum field theory (and the semiclassical approximation to
quantum gravity Quantum gravity (QG) is a field of theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, ...

quantum gravity
) in an important way, it has not been completely reconciled with these theories. Brandenberger commented on fine-tuning in another situation. The amplitude of the primordial inhomogeneities produced in inflation is directly tied to the energy scale of inflation. This scale is suggested to be around
GeV GEV may refer to: * ''G.E.V.'' (board game), a tabletop game by Steve Jackson Games * Ashe County Airport, in North Carolina, United States * Gällivare Lapland Airport, in Sweden * Generalized extreme value distribution In probability theory ...
or times the Planck energy. The natural scale is naïvely the Planck scale so this small value could be seen as another form of fine-tuning (called a hierarchy problem): the energy density given by the scalar potential is down by compared to the Planck density. This is not usually considered to be a critical problem, however, because the scale of inflation corresponds naturally to the scale of gauge unification.


Eternal inflation

In many models, the inflationary phase of the Universe's expansion lasts forever in at least some regions of the Universe. This occurs because inflating regions expand very rapidly, reproducing themselves. Unless the rate of decay to the non-inflating phase is sufficiently fast, new inflating regions are produced more rapidly than non-inflating regions. In such models, most of the volume of the Universe is continuously inflating at any given time. All models of eternal inflation produce an infinite, hypothetical multiverse, typically a fractal. The multiverse theory has created significant dissension in the scientific community about the viability of the inflationary model.
Paul Steinhardt Paul Joseph Steinhardt (born December 25, 1952) is an American theoretical physicist Theoretical physics is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Phys ...
, one of the original architects of the inflationary model, introduced the first example of eternal inflation in 1983. He showed that the inflation could proceed forever by producing bubbles of non-inflating space filled with hot matter and radiation surrounded by empty space that continues to inflate. The bubbles could not grow fast enough to keep up with the inflation. Later that same year, Alexander Vilenkin showed that eternal inflation is generic. Although new inflation is classically rolling down the potential, quantum fluctuations can sometimes lift it to previous levels. These regions in which the inflaton fluctuates upwards expand much faster than regions in which the inflaton has a lower potential energy, and tend to dominate in terms of physical volume. It has been shown that any inflationary theory with an unbounded potential is eternal. There are well-known theorems that this steady state cannot continue forever into the past. Inflationary spacetime, which is similar to de Sitter space, is incomplete without a contracting region. However, unlike de Sitter space, fluctuations in a contracting inflationary space collapse to form a gravitational singularity, a point where densities become infinite. Therefore, it is necessary to have a theory for the Universe's initial conditions. In eternal inflation, regions with inflation have an exponentially growing volume, while regions that are not inflating don't. This suggests that the volume of the inflating part of the Universe in the global picture is always unimaginably larger than the part that has stopped inflating, even though inflation eventually ends as seen by any single pre-inflationary observer. Scientists disagree about how to assign a probability distribution to this hypothetical anthropic landscape. If the probability of different regions is counted by volume, one should expect that inflation will never end or applying boundary conditions that a local observer exists to observe it, that inflation will end as late as possible. Some physicists believe this paradox can be resolved by weighting observers by their pre-inflationary volume. Others believe that there is no resolution to the paradox and that the multiverse is a critical flaw in the inflationary paradigm. Paul Steinhardt, who first introduced the eternal inflationary model, later became one of its most vocal critics for this reason.


Initial conditions

Some physicists have tried to avoid the initial conditions problem by proposing models for an eternally inflating universe with no origin. These models propose that while the Universe, on the largest scales, expands exponentially it was, is and always will be, spatially infinite and has existed, and will exist, forever. Other proposals attempt to describe the ex nihilo creation of the Universe based on quantum cosmology and the following inflation. Vilenkin put forth one such scenario. Hartle–Hawking state, Hartle and Hawking offered the no-boundary proposal for the initial creation of the Universe in which inflation comes about naturally. Guth described the inflationary universe as the "ultimate free lunch": new universes, similar to our own, are continually produced in a vast inflating background. Gravitational interactions, in this case, circumvent (but do not violate) the first law of thermodynamics (energy conservation) and the second law of thermodynamics (
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

entropy
and the arrow of time problem). However, while there is consensus that this solves the initial conditions problem, some have disputed this, as it is much more likely that the Universe came about by a
quantum fluctuation In quantum physics Quantum mechanics is a fundamental theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously m ...
. Don Page (physicist), Don Page was an outspoken critic of inflation because of this anomaly. He stressed that the thermodynamic arrow of time necessitates low
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamic ...

entropy
initial conditions, which would be highly unlikely. According to them, rather than solving this problem, the inflation theory aggravates it – the reheating at the end of the inflation era increases entropy, making it necessary for the initial state of the Universe to be even more orderly than in other Big Bang theories with no inflation phase. Hawking and Page later found ambiguous results when they attempted to compute the probability of inflation in the Hartle-Hawking initial state. Other authors have argued that, since inflation is eternal, the probability doesn't matter as long as it is not precisely zero: once it starts, inflation perpetuates itself and quickly dominates the Universe. However, Albrecht and Lorenzo Sorbo argued that the probability of an inflationary cosmos, consistent with today's observations, emerging by a random fluctuation from some pre-existent state is much higher than that of a non-inflationary cosmos. This is because the "seed" amount of non-gravitational energy required for the inflationary cosmos is so much less than that for a non-inflationary alternative, which outweighs any entropic considerations. Another problem that has occasionally been mentioned is the trans-Planckian problem or trans-Planckian effects. Since the energy scale of inflation and the Planck scale are relatively close, some of the quantum fluctuations that have made up the structure in our universe were smaller than the Planck length before inflation. Therefore, there ought to be corrections from Planck-scale physics, in particular the unknown quantum theory of gravity. Some disagreement remains about the magnitude of this effect: about whether it is just on the threshold of detectability or completely undetectable.


Hybrid inflation

Another kind of inflation, called ''hybrid inflation'', is an extension of new inflation. It introduces additional scalar fields, so that while one of the scalar fields is responsible for normal slow roll inflation, another triggers the end of inflation: when inflation has continued for sufficiently long, it becomes favorable to the second field to decay into a much lower energy state. In hybrid inflation, one scalar field is responsible for most of the energy density (thus determining the rate of expansion), while another is responsible for the slow roll (thus determining the period of inflation and its termination). Thus fluctuations in the former inflaton would not affect inflation termination, while fluctuations in the latter would not affect the rate of expansion. Therefore, hybrid inflation is not eternal. When the second (slow-rolling) inflaton reaches the bottom of its potential, it changes the location of the minimum of the first inflaton's potential, which leads to a fast roll of the inflaton down its potential, leading to termination of inflation.


Relation to dark energy

Dark energy is broadly similar to inflation and is thought to be causing the expansion of the present-day universe to accelerate. However, the energy scale of dark energy is much lower,  GeV, roughly 27 orders of magnitude less than the scale of inflation.


Inflation and string cosmology

The discovery of Compactification (physics)#Flux compactification, flux compactifications opened the way for reconciling inflation and string theory. ''Brane inflation'' suggests that inflation arises from the motion of D-branes in the compactified geometry, usually towards a stack of anti-D-branes. This theory, governed by the ''Dirac-Born-Infeld action'', is different from ordinary inflation. The dynamics are not completely understood. It appears that special conditions are necessary since inflation occurs in tunneling between two vacua in the string landscape. The process of tunneling between two vacua is a form of old inflation, but new inflation must then occur by some other mechanism.


Inflation and loop quantum gravity

When investigating the effects the theory of loop quantum gravity would have on cosmology, a loop quantum cosmology model has evolved that provides a possible mechanism for cosmological inflation. Loop quantum gravity assumes a quantized spacetime. If the energy density is larger than can be held by the quantized spacetime, it is thought to bounce back.


Alternatives and adjuncts

Other models have been advanced that are claimed to explain some or all of the observations addressed by inflation.


Big bounce

The big bounce hypothesis attempts to replace the cosmic singularity with a cosmic contraction and bounce, thereby explaining the initial conditions that led to the big bang. The flatness and horizon problems are naturally solved in the Einstein–Cartan theory, Einstein-Cartan-Sciama-Kibble theory of gravity, without needing an exotic form of matter or free parameters. This theory extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable. The minimal coupling between torsion and Dirac spinors generates a spin-spin interaction that is significant in fermionic matter at extremely high densities. Such an interaction averts the unphysical Big Bang singularity, replacing it with a cusp-like bounce at a finite minimum scale factor, before which the Universe was contracting. The rapid expansion immediately after the Big Bounce explains why the present Universe at largest scales appears spatially flat, homogeneous and isotropic. As the density of the Universe decreases, the effects of torsion weaken and the Universe smoothly enters the radiation-dominated era.


Ekpyrotic and cyclic models

The ekpyrotic and cyclic models are also considered adjuncts to inflation. These models solve the
horizon problem The horizon problem (also known as the homogeneity problem) is a cosmological Cosmology (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the He ...

horizon problem
through an expanding epoch well ''before'' the Big Bang, and then generate the required spectrum of primordial density perturbations during a contracting phase leading to a Big Crunch. The Universe passes through the Big Crunch and emerges in a hot
Big Bang The Big Bang theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously making sense of things, applying logic ...

Big Bang
phase. In this sense they are reminiscent of Richard Chace Tolman's
oscillatory universe A cyclic model (or oscillating model) is any of several cosmological model Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the ...
; in Tolman's model, however, the total age of the Universe is necessarily finite, while in these models this is not necessarily so. Whether the correct spectrum of density fluctuations can be produced, and whether the Universe can successfully navigate the Big Bang/Big Crunch transition, remains a topic of controversy and current research. Ekpyrotic models avoid the
magnetic monopole In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that departmen ...
problem as long as the temperature at the Big Crunch/Big Bang transition remains below the Grand Unified Scale, as this is the temperature required to produce magnetic monopoles in the first place. As things stand, there is no evidence of any 'slowing down' of the expansion, but this is not surprising as each cycle is expected to last on the order of a trillion years.


String gas cosmology

String theory requires that, in addition to the three observable spatial dimensions, additional dimensions exist that are curled up or compactification (physics), compactified (see also Kaluza–Klein theory). Extra dimensions appear as a frequent component of supergravity models and other approaches to
quantum gravity Quantum gravity (QG) is a field of theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict List of natural phenomena, ...

quantum gravity
. This raised the contingent question of why four space-time dimensions became large and the rest became unobservably small. An attempt to address this question, called ''string gas cosmology'', was proposed by Robert Brandenberger and Cumrun Vafa. This model focuses on the dynamics of the early universe considered as a hot gas of strings. Brandenberger and Vafa show that a dimension of spacetime can only expand if the strings that wind around it can efficiently annihilate each other. Each string is a one-dimensional object, and the largest number of dimensions in which two strings will Transversality (mathematics), generically intersect (and, presumably, annihilate) is three. Therefore, the most likely number of non-compact (large) spatial dimensions is three. Current work on this model centers on whether it can succeed in stabilizing the size of the compactified dimensions and produce the correct spectrum of primordial density perturbations. The original model did not "solve the entropy and flatness problems of standard cosmology", although Brandenburger and coauthors later argued that these problems can be eliminated by implementing string gas cosmology in the context of a bouncing-universe scenario.


Varying ''c''

Cosmological models employing a variable speed of light have been proposed to resolve the horizon problem of and provide an alternative to cosmic inflation. In the VSL models, the fundamental constant ''c'', denoting the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
in vacuum, is greater in the early universe than its present value, effectively increasing the
particle horizon The particle horizon (also called the cosmological horizon, the comoving horizon (in Dodelson's text), or the cosmic light horizon) is the maximum distance from which light from Elementary particle, particles could have traveled to the observation, ...
at the time of decoupling sufficiently to account for the observed isotropy of the CMB.


Criticisms

Since its introduction by Alan Guth in 1980, the inflationary paradigm has become widely accepted. Nevertheless, many physicists, mathematicians, and philosophers of science have voiced criticisms, claiming untestable predictions and a lack of serious empirical support. In 1999, John Earman and Jesús Mosterín published a thorough critical review of inflationary cosmology, concluding, : "we do not think that there are, as yet, good grounds for admitting any of the models of inflation into the standard core of cosmology." As pointed out by Roger Penrose from 1986 on, in order to work, inflation requires extremely specific initial conditions of its own, so that the problem (or pseudo-problem) of initial conditions is not solved: : "There is something fundamentally misconceived about trying to explain the uniformity of the early universe as resulting from a thermalization process. ... For, if the thermalization is actually doing anything ... then it represents a definite increasing of the entropy. Thus, the universe would have been even more special before the thermalization than after." The problem of specific or "fine-tuned" initial conditions would not have been solved; it would have gotten worse. At a conference in 2015, Penrose said that : "inflation isn't falsifiable, it's falsified. ... BICEP and Keck Array, BICEP did a wonderful service by bringing all the Inflation-ists out of their shell, and giving them a black eye." — This is a collation of remarks from the third day of the conference. A recurrent criticism of inflation is that the invoked inflaton field does not correspond to any known physical field, and that its potential energy curve seems to be an ad hoc contrivance to accommodate almost any data obtainable.
Paul Steinhardt Paul Joseph Steinhardt (born December 25, 1952) is an American theoretical physicist Theoretical physics is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Phys ...
, one of the founding fathers of inflationary cosmology, has recently become one of its sharpest critics. He calls 'bad inflation' a period of accelerated expansion whose outcome conflicts with observations, and 'good inflation' one compatible with them: : "Not only is bad inflation more likely than good inflation, but no inflation is more likely than either ... Roger Penrose considered all the possible configurations of the inflaton and gravitational fields. Some of these configurations lead to inflation ... Other configurations lead to a uniform, flat universe directly – without inflation. Obtaining a flat universe is unlikely overall. Penrose's shocking conclusion, though, was that obtaining a flat universe without inflation is much more likely than with inflation – by a factor of googolplex, 10 to the googol power!" Together with Anna Ijjas and Abraham Loeb, he wrote articles claiming that the inflationary paradigm is in trouble in view of the data from the Planck (spacecraft), Planck satellite. Counter-arguments were presented by
Alan Guth Alan Harvey Guth (; born February 27, 1947) is an American theoretical physicist and cosmologist. Guth has researched elementary particle theory (and how particle theory is applicable to the early universe). He is Victor Weisskopf Professor of ...
, David Kaiser, and Yasunori Nomura and by
Andrei Linde Andrei Dmitriyevich Linde (russian: Андре́й Дми́триевич Ли́нде; born March 2, 1948) is a Russian-American theoretical A theory is a rational Rationality is the quality or state of being rational – that is, being b ...

Andrei Linde
, saying that : "cosmic inflation is on a stronger footing than ever before".


See also


Notes


References


Sources


External links


Was Cosmic Inflation The 'Bang' Of The Big Bang?
by Alan Guth, 1997 *
update 2004
by Andrew Liddle * *
The Growth of Inflation
''Symmetry'', December 2004
Guth's logbook showing the original idea

WMAP Bolsters Case for Cosmic Inflation, March 2006


* Max Tegmark's ''Our Mathematical Universe'' (2014)
"Chapter 5: Inflation"
{{DEFAULTSORT:Inflation (Cosmology) Inflation (cosmology), Physical cosmology Concepts in astronomy 1980 in science