![CMB Timeline300 no WMAP](https://upload.wikimedia.org/wikipedia/commons/6/6f/CMB_Timeline300_no_WMAP.jpg)
In
cosmology
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount (lexicographer), Thomas Blount's ''Glossographia'', and in 1731 taken up in ...
, the cosmological constant (usually denoted by the Greek capital letter
lambda
Lambda (}, ''lám(b)da'') is the 11th letter of the Greek alphabet, representing the voiced alveolar lateral approximant . In the system of Greek numerals, lambda has a value of 30. Lambda is derived from the Phoenician Lamed . Lambda gave rise ...
: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
temporarily added to his
field equations
A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum ...
of
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
. He later removed it. Much later it was revived and reinterpreted as the energy density of space, or
vacuum energy
Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.
The effects of vacuum energy can be experiment ...
, that arises in
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
. It is closely associated with the concept of
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
.
Einstein originally introduced the constant in 1917 to counterbalance the effect of gravity and achieve a
static universe
In cosmology, a static universe (also referred to as stationary, infinite, static infinite or static eternal) is a cosmological model in which the universe is both spatially and temporally infinite, and space is neither expanding nor contract ...
, a notion that was the accepted view at the time. Einstein's cosmological constant was abandoned after
Edwin Hubble
Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an Americans, American astronomer. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology.
Hubble proved that many objects ...
's confirmation that the universe was expanding.
From the 1930s until the late 1990s, most physicists agreed with Einstein's choice of setting the cosmological constant to zero.
That changed with the discovery in 1998 that the
expansion of the universe is accelerating, implying that the cosmological constant may have a positive value.
Since the 1990s, studies have shown that, assuming the
cosmological principle
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throu ...
, around 68% of the mass–energy density of the universe can be attributed to so-called dark energy.
The cosmological constant is the simplest possible explanation for dark energy, and is used in the current standard model of cosmology known as the
ΛCDM model
The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a Parameter#Modelization, parameterization of the Big Bang physical cosmology, cosmological model in which the universe contains three major components: first, a cosmological constant de ...
.
According to
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 ...
(QFT), which underlies modern
particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
, empty space is defined by the
vacuum state
In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. The word zero-point field is sometimes used as ...
, which is composed of a collection of
quantum fields. All these quantum fields exhibit fluctuations in their
ground state
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. ...
(lowest energy density) arising from the
zero-point energy
Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly Quantum fluctuation, fluctuate in their lowest energy state as described by the Heisen ...
present everywhere in space. These zero-point fluctuations should act as a contribution to the cosmological constant , but when calculations are performed, these fluctuations give rise to an enormous vacuum energy. The discrepancy between theorized vacuum energy from quantum field theory and observed vacuum energy from cosmology is a source of major contention, with the values predicted exceeding observation by some 120 orders of magnitude, a discrepancy that has been called "the worst theoretical prediction in the history of physics".
This issue is called the
cosmological constant problem
In cosmology, the cosmological constant problem or vacuum catastrophe is the disagreement between the observed values of vacuum energy density (the small value of the cosmological constant) and theoretical large value of zero-point energy sugges ...
and it is one of the greatest mysteries in science with many physicists believing that "the vacuum holds the key to a full understanding of nature".
History
Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
included the cosmological constant as a term in his
field equations
A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum ...
for
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
because he was dissatisfied that otherwise his equations did not allow for a
static universe
In cosmology, a static universe (also referred to as stationary, infinite, static infinite or static eternal) is a cosmological model in which the universe is both spatially and temporally infinite, and space is neither expanding nor contract ...
: gravity would cause a universe that was initially non-expanding to contract. To counteract this possibility, Einstein added the cosmological constant.
However, soon after Einstein developed his static theory, observations by
Edwin Hubble
Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an Americans, American astronomer. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology.
Hubble proved that many objects ...
indicated that the universe appears to be expanding; this was consistent with a cosmological solution to the ''original'' general relativity equations that had been found by the mathematician
Friedmann, working on the Einstein equations of general relativity. Einstein reportedly referred to his failure to accept the validation of his equations—when they had predicted the expansion of the universe in theory, before it was demonstrated in observation of the cosmological
redshift
In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation (such as light). The opposite change, a decrease in wavelength and simultaneous increase in f ...
—as his "biggest blunder".
It transpired that adding the cosmological constant to Einstein's equations does not lead to a static universe at equilibrium because the
equilibrium is unstable: if the universe expands slightly, then the expansion releases
vacuum energy
Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.
The effects of vacuum energy can be experiment ...
, which causes yet more expansion. Likewise, a universe that contracts slightly will continue contracting.
However, the cosmological constant remained a subject of theoretical and empirical interest. Empirically, the cosmological data of recent decades strongly suggests that our universe has a positive cosmological constant.
The explanation of this small but positive value is a remaining theoretical challenge, the so-called
cosmological constant problem
In cosmology, the cosmological constant problem or vacuum catastrophe is the disagreement between the observed values of vacuum energy density (the small value of the cosmological constant) and theoretical large value of zero-point energy sugges ...
.
Some early generalizations of Einstein's gravitational theory, known as
classical unified field theories
Since the 19th century, some physicists, notably Albert Einstein, have attempted to develop a single theoretical framework that can account for all the fundamental forces of nature – a unified field theory. Classical unified field theories are at ...
, either introduced a cosmological constant on theoretical grounds or found that it arose naturally from the mathematics. For example, Sir
Arthur Stanley Eddington
Sir Arthur Stanley Eddington (28 December 1882 – 22 November 1944) was an English astronomer, physicist, and mathematician. He was also a philosopher of science and a populariser of science. The Eddington limit, the natural limit to the lumi ...
claimed that the cosmological constant version of the vacuum field equation expressed the "
epistemological
Epistemology (; ), or the theory of knowledge, is the branch of philosophy concerned with knowledge. Epistemology is considered a major subfield of philosophy, along with other major subfields such as ethics, logic, and metaphysics.
Episte ...
" property that the universe is "self-
gauging", and
Erwin Schrödinger
Erwin Rudolf Josef Alexander Schrödinger (, ; ; 12 August 1887 – 4 January 1961), sometimes written as or , was a Nobel Prize-winning Austrian physicist with Irish citizenship who developed a number of fundamental results in quantum theory ...
's pure-
affine
Affine may describe any of various topics concerned with connections or affinities.
It may refer to:
* Affine, a relative by marriage in law and anthropology
* Affine cipher, a special case of the more general substitution cipher
* Affine comb ...
theory using a simple
variational principle
In science and especially in mathematical studies, a variational principle is one that enables a problem to be solved using calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those func ...
produced the field equation with a cosmological term.
Sequence of events 1915–1998
* In 1915, Einstein publishes his equations of
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, without a cosmological constant .
* In 1917, Einstein adds the parameter to his equations when he realizes that his theory implies a dynamic universe for which space is function of time. He then gives this constant a value that makes his Universe model remain static and eternal (Einstein static universe).
* In 1922, the Russian physicist
Alexander Friedmann
Alexander Alexandrovich Friedmann (also spelled Friedman or Fridman ; russian: Алекса́ндр Алекса́ндрович Фри́дман) (June 16 .S. 4 1888 – September 16, 1925) was a Russian and Soviet physicist and mathematician ...
mathematically shows that Einstein's equations (whatever ) remain valid in a dynamic universe.
* In 1927, the Belgian astrophysicist
Georges Lemaître
Georges Henri Joseph Édouard Lemaître ( ; ; 17 July 1894 – 20 June 1966) was a Belgian Catholic priest, theoretical physicist, mathematician, astronomer, and professor of physics at the Catholic University of Louvain. He was the first to th ...
shows that the Universe is expanding by combining general relativity with astronomical observations, those of Hubble in particular.
* In 1931, Einstein accepts the theory of an expanding universe and proposes, in 1932 with the Dutch physicist and astronomer
Willem de Sitter, a model of a continuously expanding Universe with zero cosmological constant (Einstein–de Sitter spacetime).
* In 1998, two teams of astrophysicists, one led by
Saul Perlmutter
Saul Perlmutter (born September 22, 1959) is a U.S. astrophysicist at the Lawrence Berkeley National Laboratory and a professor of physics at the University of California, Berkeley. He is a member of both the American Academy of Arts & Sciences ...
, the other led by
Brian Schmidt
Brian Paul Schmidt (born 24 February 1967) is the Vice-Chancellor of the Australian National University (ANU). He was previously a Distinguished Professor, Australian Research Council Laureate Fellow and astrophysicist at the University's Mo ...
and
Adam Riess
Adam Guy Riess (born December 16, 1969) is an American astrophysicist and Bloomberg Distinguished Professor at Johns Hopkins University and the Space Telescope Science Institute. He is known for his research in using supernovae as cosmologica ...
, carried out measurements on distant supernovae which showed that the speed of galaxies' recession in relation to the
Milky Way
The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...
increases over time. The universe is in accelerated expansion, which requires having a strictly positive . The universe would contain a mysterious
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
producing a repulsive force that counterbalances the gravitational braking produced by the matter contained in the universe (see ''
Standard cosmological model
The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parameterization of the Big Bang cosmological model in which the universe contains three major components: first, a cosmological constant denoted by Lambda (Greek Λ) associated with ...
'').
:For this work,
Perlmutter,
Schmidt
Schmidt may refer to:
* Schmidt (surname), including list of people with the surname
* Schmidt (singer) (born 1990), German pop and jazz singer
* Schmidt (lunar crater), a small lunar impact crater
* Schmidt (Martian crater), a List of craters on ...
, and
Riess jointly received the Nobel Prize in physics in 2011.
Equation
![080998 Universe Content 240 after Planck](https://upload.wikimedia.org/wikipedia/commons/b/b6/080998_Universe_Content_240_after_Planck.jpg)
The cosmological constant appears in the
Einstein field equations
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it.
The equations were published by Einstein in 1915 in the form ...
in the form
:
where
the Ricci tensor , Ricci scalar and the
metric tensor
In the mathematical field of differential geometry, a metric tensor (or simply metric) is an additional structure on a manifold (such as a surface) that allows defining distances and angles, just as the inner product on a Euclidean space allows ...
describe the structure of
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
, the
stress–energy tensor
The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress ...
describes the energy density, momentum density and stress at that point in spacetime, and . The
gravitational constant
The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
and the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
are universal constants. When is zero, this reduces to the field equation of general relativity usually used in the 20th century. When is zero, the field equation describes empty space (a
vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
).
The cosmological constant has the same effect as an intrinsic
energy density
In physics, energy density is the amount of energy stored in a given system or region of space per unit volume. It is sometimes confused with energy per unit mass which is properly called specific energy or .
Often only the ''useful'' or extract ...
of the vacuum, (and an associated
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
). In this context, it is commonly moved to the right-hand side of the equation using . It is common to quote values of energy density directly, though still using the name "cosmological constant". The dimension of is generally understood as length.
Using the values known in 2018 and Planck units for = and the
Hubble constant
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...
0 = = ,
has the value of
:
where
is the
Planck length. A positive vacuum energy density resulting from a cosmological constant implies a negative pressure, and vice versa. If the energy density is positive, the associated negative pressure will drive an accelerated expansion of the universe, as observed. (See ''
Dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
'' and ''
Cosmic inflation
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singularity ...
'' for details.)
(Omega sub Lambda)
Instead of the cosmological constant itself, cosmologists often refer to the ratio between the energy density due to the cosmological constant and the
critical density of the universe, the tipping point for a sufficient density to stop the universe from expanding forever. This ratio is usually denoted by and is estimated to be , according to results published by the
Planck Collaboration in 2018.
In a flat universe, is the fraction of the energy of the universe due to the cosmological constant, i.e., what we would intuitively call the fraction of the universe that is made up of dark energy. Note that this value changes over time: The critical density changes with
cosmological time
Cosmic time, or cosmological time, is the time coordinate commonly used in the Big Bang models of physical cosmology. Such time coordinate may be defined for a homogeneous, expanding universe so that the universe has the same density everywhere at ...
but the energy density due to the cosmological constant remains unchanged throughout the history of the universe, because the amount of dark energy increases as the universe grows but the amount of matter does not.
Equation of state
Another ratio that is used by scientists is the
equation of state
In physics, chemistry, and thermodynamics, an equation of state is a thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, volume, temperature, or internal ...
, usually denoted , which is the ratio of pressure that dark energy puts on the universe to the energy per unit volume. This ratio is for the cosmological constant used in the Einstein equations; alternative time-varying forms of vacuum energy such as
quintessence generally use a different value. The value = , measured by the Planck Collaboration (2018)
[ is consistent with , assuming does not change over cosmic time.
]
Positive value
Observations announced in 1998 of distance–redshift relation for Type Ia supernovae
A Type Ia supernova (read: "type one-A") is a type of supernova that occurs in binary systems (two stars orbiting one another) in which one of the stars is a white dwarf. The other star can be anything from a giant star to an even smaller white ...
indicated that the expansion of the universe is accelerating, if one assumes the cosmological principle
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throu ...
. When combined with measurements of the cosmic microwave background radiation
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all space ...
these implied a value of ≈ 0.7, a result which has been supported and refined by more recent measurements (as well as previous works). If one assumes the cosmological principle
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throu ...
, as in the case for all models that use the Friedmann–Lemaître–Robertson–Walker metric
The Friedmann–Lemaître–Robertson–Walker (FLRW; ) metric is a metric based on the exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe tha ...
, while there are other possible causes of an accelerating universe
Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered duri ...
, such as quintessence, the cosmological constant is in most respects the simplest solution. Thus, the Lambda-CDM model
The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a parameterization of the Big Bang cosmological model in which the universe contains three major components: first, a cosmological constant denoted by Lambda (Greek Λ) associated with d ...
, the current standard model of cosmology which uses the FLRW metric, includes the cosmological constant, which is measured to be on the order of . It may be expressed as (by multiplication with , i.e. ≈) or as 10−122 ''ℓ''−2 (where ''ℓ'' is the Planck length). The value is based on recent measurements of vacuum energy density, = ≘ = . However, due to the Hubble tension
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving ...
and the CMB dipole
In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is homogeneity (physics), homogeneous and Isotropy, isotropic when viewed on a large enough scale, since the forces ar ...
, recently it has been proposed that the cosmological principle is no longer true in the late universe and that the FLRW metric breaks down, so it is possible that observations usually attributed to an accelerating universe are simply a result of the cosmological principle not applying in the late universe.
As was only recently seen, by works of 't Hooft, Susskind and others, a positive cosmological constant has surprising consequences, such as a finite maximum 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 thermodynam ...
of the observable universe (see ''Holographic principle
The holographic principle is an axiom in string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — such as a ...
'').
Predictions
Quantum field theory
A major outstanding problem is that most quantum field theories
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 ...
predict a huge value for the quantum vacuum
In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. The word zero-point field is sometimes used as ...
. A common assumption is that the quantum vacuum
In quantum field theory, the quantum vacuum state (also called the quantum vacuum or vacuum state) is the quantum state with the lowest possible energy. Generally, it contains no physical particles. The word zero-point field is sometimes used as ...
is equivalent to the cosmological constant. Although no theory exists that supports this assumption, arguments can be made in its favor.
Such arguments are usually based on dimensional analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as m ...
and effective field theory
In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model. An effective field theory includes the appropriate degrees ...
. If the universe is described by an effective local quantum field theory down to the Planck scale, then we would expect a cosmological constant of the order of ( in reduced Planck units). As noted above, the measured cosmological constant is smaller than this by a factor of ~10120. This discrepancy has been called "the worst theoretical prediction in the history of physics".
Some supersymmetric
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...
theories require a cosmological constant that is exactly zero, which further complicates things. This is the cosmological constant problem
In cosmology, the cosmological constant problem or vacuum catastrophe is the disagreement between the observed values of vacuum energy density (the small value of the cosmological constant) and theoretical large value of zero-point energy sugges ...
, the worst problem of 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 ...
in physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
: there is no known natural way to derive the tiny cosmological constant used in cosmology
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount (lexicographer), Thomas Blount's ''Glossographia'', and in 1731 taken up in ...
from particle physics
Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...
.
No vacuum in the string theory landscape
The string theory landscape or landscape of vacua refers to the collection of possible false vacua in string theory,The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10500. See M. Douglas, "The ...
is known to support a metastable, positive cosmological constant, and in 2018 a group of four physicists advanced a controversial conjecture which would imply that no such universe exists.
Anthropic principle
One possible explanation for the small but non-zero value was noted by Steven Weinberg
Steven Weinberg (; May 3, 1933 – July 23, 2021) was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interactio ...
in 1987 following the anthropic principle
The anthropic principle, also known as the "observation selection effect", is the hypothesis, first proposed in 1957 by Robert Dicke, that there is a restrictive lower bound on how statistically probable our observations of the universe are, beca ...
. Weinberg explains that if the vacuum energy took different values in different domains of the universe, then observers would necessarily measure values similar to that which is observed: the formation of life-supporting structures would be suppressed in domains where the vacuum energy is much larger. Specifically, if the vacuum energy is negative and its absolute value is substantially larger than it appears to be in the observed universe (say, a factor of 10 larger), holding all other variables (e.g. matter density) constant, that would mean that the universe is closed; furthermore, its lifetime would be shorter than the age of our universe, possibly too short for intelligent life to form. On the other hand, a universe with a large positive cosmological constant would expand too fast, preventing galaxy formation. According to Weinberg, domains where the vacuum energy is compatible with life would be comparatively rare. Using this argument, Weinberg predicted that the cosmological constant would have a value of less than a hundred times the currently accepted value. In 1992, Weinberg refined this prediction of the cosmological constant to 5 to 10 times the matter density.
This argument depends on the vacuum energy density being constant throughout spacetime, as would be expected if dark energy were the cosmological constant. There is no evidence that the vacuum energy does vary, but it may be the case if, for example, the vacuum energy is (even in part) the potential of a scalar field such as the residual inflaton
The inflaton field is a hypothetical scalar field which is conjectured to have driven cosmic inflation in the very early universe.
The field, originally postulated by Alan Guth, provides a mechanism by which a period of rapid expansion from 10& ...
(also see '' Quintessence''). Another theoretical approach that deals with the issue is that of multiverse
The multiverse is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describe them. The di ...
theories, which predict a large number of "parallel" universes with different laws of physics and/or values of fundamental constants. Again, the anthropic principle states that we can only live in one of the universes that is compatible with some form of intelligent life. Critics claim that these theories, when used as an explanation for fine-tuning, commit the inverse gambler's fallacy
The inverse gambler's fallacy, named by philosopher Ian Hacking, is a formal fallacy of Bayesian inference which is an inverse of the better known gambler's fallacy. It is the fallacy of concluding, on the basis of an unlikely outcome of a rando ...
.
In 1995, Weinberg's argument was refined by Alexander Vilenkin
Alexander Vilenkin (russian: Алекса́ндр Виле́нкин; uk, Олександр Віленкін; born 13 May 1949) is the Leonard Jane Holmes Bernstein Professor of Evolutionary Science and Director of the Institute of Cosmology a ...
to predict a value for the cosmological constant that was only ten times the matter density, i.e. about three times the current value since determined.
Failure to detect dark energy
An attempt to directly observe dark energy in a laboratory failed to detect a new force. Inferring the presence of dark energy through its interaction with baryons in the cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
has also led to a negative result, although the current analyses have been derived only at the linear perturbation regime.
See also
* Big Rip
In physical cosmology, the Big Rip is a hypothetical cosmological model concerning the ultimate fate of the universe, in which the matter of the universe, from stars and galaxies to atoms and subatomic particles, and even spacetime itself, is ...
* Higgs mechanism
In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other bein ...
* Lambdavacuum solution
* Naturalness (physics)
In physics, naturalness is the aesthetic property that the dimensionless ratios between free parameters or physical constants appearing in a physical theory should take values "of order 1" and that free parameters are not fine-tuned. That is, a n ...
* Quantum electrodynamics
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
* de Sitter invariant special relativity
In mathematical physics, de Sitter invariant special relativity is the speculative idea that the fundamental symmetry group of spacetime is the indefinite orthogonal group SO(4,1), that of de Sitter space. In the standard theory of general relativ ...
* Unruh effect
The Unruh effect (also known as the Fulling–Davies–Unruh effect) is a kinematic prediction of quantum field theory that an accelerating observer will observe a thermal bath, like blackbody radiation, whereas an inertial observer would observe ...
References
Footnotes
Bibliography
Primary literature
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Secondary literature: review articles, monographs and textbooks
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External links
* Michael, E., University of Colorado, Department of Astrophysical and Planetary Sciences,
The Cosmological Constant
* Carroll, Sean M.,
"The Cosmological Constant"
' (short),
"The Cosmological Constant"
'(extended).
News story: More evidence for dark energy being the cosmological constant
Cosmological constant
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{{DEFAULTSORT:Cosmological Constant
Physical cosmology
Big Bang
General relativity
Theories of gravity
Albert Einstein
Astronomical hypotheses
Dark energy