The expansion of the universe is the increase in
distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
between any two given
gravitationally unbound parts of the
observable universe
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 ob ...
with time.
It is an
intrinsic
In science and engineering, an intrinsic property is a property of a specified subject that exists itself or within the subject. An extrinsic property is not essential or inherent to the subject that is being characterized. For example, mass ...
expansion whereby the scale of space itself changes. The universe does not expand "into" anything and does not require space to exist "outside" it. This expansion involves neither space nor objects in space "moving" in a traditional sense, but rather it is the metric (which governs the size and geometry of spacetime itself) that changes in scale. As the spatial part of the universe's
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 differ ...
metric
Metric or metrical may refer to:
* Metric system, an internationally adopted decimal system of measurement
* An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement
Mathematics
In mathem ...
increases in scale, objects become more distant from one another at ever-increasing speeds. To any observer in the universe, it appears that all of space is expanding, and that all but
the nearest galaxies (which are bound by gravity) recede at
speeds that are proportional to their distance from the observer. While objects within space cannot travel
faster than light
Faster-than-light (also FTL, superluminal or supercausal) travel and communication are the conjectural propagation of matter or information faster than the speed of light (). The special theory of relativity implies that only particles with zero ...
, this limitation does not apply to the effects of changes in the metric itself.
[Although anything in a ]local
Local may refer to:
Geography and transportation
* Local (train), a train serving local traffic demand
* Local, Missouri, a community in the United States
* Local government, a form of public administration, usually the lowest tier of administrat ...
reference frame
In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both mathe ...
cannot accelerate past the speed of light, this limitation does not restrict the expansion of the metric itself. Objects that recede beyond the
cosmic event horizon will eventually become unobservable, as no new light from them will be capable of overcoming the universe's expansion, limiting the size of our
observable universe
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 ob ...
.
As an effect 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 ...
, the expansion of the universe is different from the
expansion
Expansion may refer to:
Arts, entertainment and media
* ''L'Expansion'', a French monthly business magazine
* ''Expansion'' (album), by American jazz pianist Dave Burrell, released in 2004
* ''Expansions'' (McCoy Tyner album), 1970
* ''Expansio ...
s and
explosions seen in daily life. It is a property of the
universe as a whole and occurs throughout the universe, rather than happening just to one part of the universe. Therefore, unlike other expansions and explosions, it cannot be observed from "outside" of it; it is believed that there is no "outside" to observe from.
Metric expansion is a key feature of
Big Bang cosmology
The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
, is modeled mathematically with 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 ...
and is a generic property of the universe we inhabit. However, the model is valid only on large scales (roughly the scale of
galaxy cluster
A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. They are the second-lar ...
s and above), because
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
binds matter together strongly enough that metric expansion cannot be observed on a smaller scale at this time. As such, the only galaxies receding from one another as a result of metric expansion are those separated by cosmologically relevant scales larger than the
length scales associated with the gravitational collapse that are possible in the
age of the universe
In physical cosmology, the age of the universe is the time elapsed since the Big Bang. Astronomers have derived two different measurements of the age of the universe:
a measurement based on direct observations of an early state of the universe, ...
given the
matter density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...
and average expansion rate.
According to
inflation theory, during the
inflationary epoch
__NOTOC__
In physical cosmology, the inflationary epoch was the period in the evolution of the early universe when, according to inflation theory, the universe underwent an extremely rapid exponential expansion. This rapid expansion increased the ...
about 10
−32 of a second after the
Big Bang, the universe suddenly expanded, and its volume increased by a factor of at least 10
78 (an expansion of distance by a factor of at least 10
26 in each of the three dimensions). This would be equivalent to expanding an object 1
nanometer (10
−9 m, about half the width of a
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...
of
DNA) in length to one approximately 10.6
light years
A light-year, alternatively spelled light year, is a large unit of length used to express astronomical distances and is equivalent to about 9.46 trillion kilometers (), or 5.88 trillion miles ().One trillion here is taken to be 1012 ...
(about 10
17 m or 62 trillion miles) long. A much slower and gradual expansion of space continued after this, until at around 9.8 billion years after the Big Bang (4 billion years ago) it began to gradually
expand more quickly, and is still doing so. Physicists have postulated the existence 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 univ ...
, appearing as a
cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that Albert Einstein temporarily added to his field eq ...
in the simplest gravitational models, as a way to explain this late-time acceleration. According to the simplest extrapolation of the currently favored cosmological model, 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 ...
, this acceleration becomes more dominant into the future. In June 2016,
NASA
The National Aeronautics and Space Administration (NASA ) is an independent agencies of the United States government, independent agency of the US federal government responsible for the civil List of government space agencies, space program ...
and
ESA
, owners =
, headquarters = Paris, Île-de-France, France
, coordinates =
, spaceport = Guiana Space Centre
, seal = File:ESA emblem seal.png
, seal_size = 130px
, image = Views in the Main Control Room (120 ...
scientists reported that the universe was found to be expanding 5% to 9% faster than thought earlier, based on studies using the
Hubble Space Telescope
The Hubble Space Telescope (often referred to as HST or Hubble) is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. It was not the first space telescope, but it is one of the largest and most vers ...
.
History
In 1912,
Vesto Slipher
Vesto Melvin Slipher (; November 11, 1875 – November 8, 1969) was an American astronomer who performed the first measurements of radial velocities for galaxies. He was the first to discover that distant galaxies are redshifted, thus providing t ...
discovered that light from remote galaxies was
redshifted, which was
later interpreted as galaxies receding from the Earth. In 1922,
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 ...
used
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 ...
to provide theoretical evidence that the universe is expanding.
Swedish astronomer
Knut Lundmark
Knut Emil Lundmark (14 June 1889 in Älvsbyn, Sweden – 23 April 1958 in Lund, Sweden), was a Swedish astronomer, professor of astronomy and head of the observatory at Lund University from 1929 to 1955.
Lundmark received his astronomical edu ...
was the first person to find observational evidence for expansion in 1924. According to Ian Steer of the NASA/IPAC Extragalactic Database of Galaxy Distances, "Lundmark's extragalactic distance estimates were far more accurate than Hubble's, consistent with an expansion rate (Hubble constant) that was within 1% of the best measurements today."
In 1927,
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 t ...
independently reached a similar conclusion to Friedmann on a theoretical basis, and also presented observational evidence for a
linear relationship between distance to galaxies and their recessional velocity.
Edwin Hubble observationally confirmed Lundmark's and Lemaître's findings in 1929. 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 ...
, these findings would imply that all galaxies are moving away from each other.
Based on large quantities of experimental observation and theoretical work, the
scientific consensus is that ''space itself is expanding'', and that it
expanded very rapidly within the first fraction of a second after the
Big Bang, approximately 13.8 billion years ago. This kind of expansion is known as "metric expansion". In mathematics and physics, a "
metric
Metric or metrical may refer to:
* Metric system, an internationally adopted decimal system of measurement
* An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement
Mathematics
In mathem ...
" means a measure of distance, and the term implies that ''the sense of distance within the universe is itself changing''.
On 13 January 1994, NASA formally announced a completion of its repairs on the main mirror of the
Hubble Space Telescope
The Hubble Space Telescope (often referred to as HST or Hubble) is a space telescope that was launched into low Earth orbit in 1990 and remains in operation. It was not the first space telescope, but it is one of the largest and most vers ...
allowing for sharper images and, consequently, more accurate analyses of its observations. Briefly after the repairs were made,
Wendy Freedman's 1994 Key Project analyzed the recession velocity of M100 from the core of the Virgo cluster, offering a
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 ...
measurement of 80±17 km s
-1 Mpc
-1 (Mega
Parsec
The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, an ...
). Later the same year,
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 cosmologic ...
et al utilized an empirical method of visual band light shape curves to more finely estimate the luminosity of
Type Ia supernova
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 ...
. This further minimized the systemic measurement errors of the Hubble constant to 67±7 km s
-1 Mpc
-1. Reiss's measurements on the recession velocity of the nearby Virgo cluster more closely agree with subsequent and independent analyses of
Cepheid variable
A Cepheid variable () is a type of star that pulsates radially, varying in both diameter and temperature and producing changes in brightness with a well-defined stable period and amplitude.
A strong direct relationship between a Cepheid vari ...
calibrations of 1a supernovae, which estimates a Hubble Constant of 73±7km s
-1 Mpc
-1. Within the next decade, in 2003,
David Spergel
David Nathaniel Spergel is an American theoretical astrophysicist and the Emeritus Charles A. Young Professor of Astronomy on the Class of 1897 Foundation at Princeton University. Since 2021, he has been the President of the Simons Foundation ...
's analysis of 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 ...
during the first year observations of the ''Wilkinson Microwave Anisotropy Probe'' satellite (WMAP) further agreed with the estimated expansion rates for local galaxies, 72±5 km s
-1 Mpc
-1.
Cosmic inflation
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, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net north or south "magneti ...
are seen today. Guth found in his investigation 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 grass ...
that has a positive-energy
false vacuum
In quantum field theory, a false vacuum is a hypothetical vacuum that is relatively stable, but not in the most stable state possible. This condition is known as metastable. It may last for a very long time in that state, but could eventually ...
state, then according to
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 ...
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 as 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
The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
. According to
Roger Penrose, inflation does not solve the main problem it was supposed to solve, namely the incredibly low entropy (with ''unlikeliness'' of the state on the order of 1/10
10128 ) of the early Universe contained in the ''gravitational conformal degrees of freedom'' (in contrast to fields degrees of freedom, such like 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 ...
whose smoothness can be explained by inflation). Thus, he puts forward his scenario of the evolution of the Universe:
conformal cyclic cosmology
Conformal cyclic cosmology (CCC) is a cosmological model in the framework of general relativity and proposed by theoretical physicist Roger Penrose. In CCC, the universe iterates through infinite cycles, with the future timelike infinity (i.e. the ...
.
No field responsible for cosmic inflation has been discovered. However such a field, if found in the future, 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 ...
. The first similar
scalar field proven to exist 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
quanta (the
subatomic particles related to it) have been named ''
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&m ...
''. 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.
Overview of metrics and comoving coordinates
To understand the metric expansion of the universe, it is helpful to discuss briefly what a metric is, and how metric expansion works.
A
metric
Metric or metrical may refer to:
* Metric system, an internationally adopted decimal system of measurement
* An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement
Mathematics
In mathem ...
defines the concept of
distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
, by stating in mathematical terms how distances between two nearby points in space are measured, in terms of the
coordinate system. Coordinate systems locate points in a space (of whatever number of
dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coor ...
s) by assigning unique positions on a grid, known as
coordinate
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sign ...
s, to each point.
Latitude
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...
and
longitude
Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lette ...
, and
x-y graphs are common examples of coordinates. A metric is a
formula that describes how a number known as "distance" is to be measured between two points.
It may seem obvious that distance is measured by a straight line, but in many cases it is not. For example,
long haul
In aviation, the flight length refers to the distance of a flight. Commercial flights are often categorized into long-, medium- or short-haul by commercial airlines based on flight length, although there is no international standard definition and ...
aircraft travel along a curve known as a "
great circle" and not a straight line, because that is a better metric for air travel. (A straight line would go through the earth). Another example is planning a car journey, where one might want the shortest journey in terms of travel time - in that case a straight line is a poor choice of metric because the shortest distance by road is not normally a straight line, and even the path nearest to a straight line will not necessarily be the quickest. A final example is the
internet
The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a '' network of networks'' that consists of private, pub ...
, where even for nearby towns, the quickest route for data can be via major connections that go across the country and back again. In this case the metric used will be the shortest time that data takes to travel between two points on the network.
In cosmology, we cannot use a ruler to measure metric expansion, because our ruler's internal forces easily overcome the extremely slow expansion of space, leaving the ruler intact. Also, any objects on or near earth that we might measure are being held together or pushed apart by several forces that are far larger in their effects. So even if we could measure the tiny expansion that is still happening, we would not notice the change on a small scale or in everyday life. On a large intergalactic scale, we can use other tests of distance and these ''do'' show that space is expanding, even if a ruler on earth could not measure it.
The metric expansion of space is described using the mathematics of
metric
Metric or metrical may refer to:
* Metric system, an internationally adopted decimal system of measurement
* An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement
Mathematics
In mathem ...
tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...
s. The coordinate system we use is called "
comoving coordinates", a type of coordinate system that takes account of
time as well as space 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 ...
, and allows us to incorporate the effects of both
general
A general officer is an officer of high rank in the armies, and in some nations' air forces, space forces, and marines or naval infantry.
In some usages the term "general officer" refers to a rank above colonel."general, adj. and n.". OED ...
and
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws ...
.
Example: "Great Circle" metric for Earth's surface
For example, consider the measurement of distance between two places on the surface of the Earth. This is a simple, familiar example of
spherical geometry. Because the surface of the Earth is two-dimensional, points on the surface of the Earth can be specified by two coordinates – for example, the latitude and longitude. Specification of a metric requires that one first specify the coordinates used. In our simple example of the surface of the Earth, we could choose any kind of coordinate system we wish, for example
latitude
In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north pol ...
and
longitude
Longitude (, ) is a geographic coordinate that specifies the east– west position of a point on the surface of the Earth, or another celestial body. It is an angular measurement, usually expressed in degrees and denoted by the Greek lette ...
, or X-Y-Z
Cartesian coordinates. Once we have chosen a specific coordinate system, the numerical values of the coordinates of any two points are uniquely determined, and based upon the properties of the space being discussed, the appropriate metric is mathematically established too. On the curved surface of the Earth, we can see this effect in long-haul
airline
An airline is a company that provides air transport services for traveling passengers and freight. Airlines use aircraft to supply these services and may form partnerships or alliances with other airlines for codeshare agreements, in wh ...
flights where the distance between two points is measured based upon a
great circle, rather than the straight line one might plot on a two-dimensional map of the Earth's surface. In general, such shortest-distance paths are called "
geodesics". In
Euclidean geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms ...
, the geodesic is a straight line, while in
non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean g ...
such as on the Earth's surface, this is not the case. Indeed, even the shortest-distance great circle path is always longer than the Euclidean straight line path which passes through the interior of the Earth. The difference between the straight line path and the shortest-distance great circle path is due to the
curvature of the Earth's surface. While there is always an effect due to this curvature, at short distances the effect is small enough to be unnoticeable.
On plane maps, great circles of the Earth are mostly not shown as straight lines. Indeed, there is a seldom-used
map projection
In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longit ...
, namely the
gnomonic projection, where all great circles are shown as straight lines, but in this projection, the distance scale varies very much in different areas. There is no map projection in which the distance between any two points on Earth, measured along the great circle geodesics, is directly proportional to their distance on the map; such accuracy is possible only with a globe.
Metric tensors
In
differential geometry, the backbone mathematics 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 ...
, a
metric tensor can be defined that precisely characterizes the space being described by explaining the way distances should be measured in every possible direction. General relativity necessarily invokes a metric in four dimensions (one of time, three of space) because, in general, different reference frames will experience different
intervals
Interval may refer to:
Mathematics and physics
* Interval (mathematics), a range of numbers
** Partially ordered set#Intervals, its generalization from numbers to arbitrary partially ordered sets
* A statistical level of measurement
* Interval e ...
of time and space depending on the
inertial frame. This means that the metric tensor in general relativity relates precisely how two
event
Event may refer to:
Gatherings of people
* Ceremony, an event of ritual significance, performed on a special occasion
* Convention (meeting), a gathering of individuals engaged in some common interest
* Event management, the organization of e ...
s in
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 differ ...
are separated.
A metric expansion occurs when the metric tensor changes with
time
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, ...
(and, specifically, whenever the spatial part of the metric gets larger as time goes forward). This kind of expansion is different from all kinds of
expansion
Expansion may refer to:
Arts, entertainment and media
* ''L'Expansion'', a French monthly business magazine
* ''Expansion'' (album), by American jazz pianist Dave Burrell, released in 2004
* ''Expansions'' (McCoy Tyner album), 1970
* ''Expansio ...
s and
explosions commonly seen in
nature
Nature, in the broadest sense, is the physical world or universe. "Nature" can refer to the phenomena of the physical world, and also to life in general. The study of nature is a large, if not the only, part of science. Although humans are ...
in no small part because times and
distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). ...
s are not the same in all reference frames, but are instead subject to change. A useful visualization is,rather than imagining objects in a fixed "space" moving apart into "emptiness", instead imagine space itself growing between all objects, without any
acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...
or movement of the objects themselves. The space between objects shrinks or grows as the various
geodesics converge or diverge.
Because this expansion is caused by relative changes in the distance-defining metric, this expansion (and the resultant movement apart of objects) is not restricted by 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 ...
upper bound
In mathematics, particularly in order theory, an upper bound or majorant of a subset of some preordered set is an element of that is greater than or equal to every element of .
Dually, a lower bound or minorant of is defined to be an eleme ...
of
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws ...
. Two reference frames that are globally separated can be moving apart faster than light without violating special relativity, although whenever two reference frames diverge from each other faster than the speed of light, there will be observable effects associated with such situations including the existence of various
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, the expanding universe, and the physics of Big Bang cosmology. Co ...
s.
Theory and observations suggest that very early in the history of the universe, there was an
inflationary Inflationism is a heterodox economic, fiscal, or monetary policy, that predicts that a substantial level of inflation is harmless, desirable or even advantageous. Similarly, inflationist economists advocate for an inflationist policy.
Mainstream ec ...
phase where the metric changed very rapidly, and that the remaining time-dependence of this metric is what we observe as the so-called
Hubble expansion, the moving apart of all gravitationally unbound objects in the universe. The expanding universe is therefore a fundamental feature of the universe we inhabit – a universe fundamentally different from the
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 ...
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 ...
first considered when he developed his gravitational theory.
Comoving coordinates
In expanding space,
proper distances are dynamical quantities that change with time. An easy way to correct for this is to use
comoving coordinates, which remove this feature and allow for a characterization of different locations in the universe without having to characterize the physics associated with metric expansion. In comoving coordinates, the distances between all objects are fixed and the instantaneous
dynamics 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, which are made up of interacting subatomic part ...
and
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 te ...
are determined by the normal
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 ...
of
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
and
electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) li ...
. Any time-evolution however must be accounted for by taking into account the
Hubble law
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 a ...
expansion in the appropriate equations in addition to any other effects that may be operating (
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
,
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 univ ...
, or
curvature, for example). Cosmological simulations that run through significant fractions of the universe's history therefore must include such effects in order to make applicable predictions for
observational cosmology
Observational cosmology is the study of the structure, the evolution and the origin of the universe through observation, using instruments such as telescopes and cosmic ray detectors.
Early observations
The science of physical cosmology as it is ...
.
Understanding the expansion of the universe
Measurement of expansion and change of rate of expansion
![Redshift blueshift](https://upload.wikimedia.org/wikipedia/commons/e/e4/Redshift_blueshift.svg)
In principle, the expansion of the universe could be measured by taking a standard ruler and measuring the distance between two cosmologically distant points, waiting a certain time, and then measuring the distance again, but in practice, standard rulers are not easy to find on cosmological scales and the timescales over which a measurable expansion would be visible are too great to be observable even by multiple generations of humans. The expansion of space is measured indirectly. The
theory of relativity
The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
predicts phenomena associated with the expansion, notably the
redshift-versus-distance relationship known as
Hubble's Law
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 a ...
; functional forms for
cosmological distance measurements that differ from what would be expected if space were not expanding; and an observable change in the
matter and energy density of the universe seen at different
lookback time
Before Present (BP) years, or "years before present", is a time scale used mainly in archaeology, geology and other scientific disciplines to specify when events occurred relative to the origin of practical radiocarbon dating in the 1950s. Becau ...
s.
The first measurement of the expansion of space came with Hubble's realization of the velocity vs. redshift relation. Most recently, by comparing the apparent brightness of distant
standard candles to the redshift of their host galaxies, the expansion rate of the universe has been measured to be
H0 = .
This means that for every million
parsec
The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, an ...
s of distance from the observer, the light received from that distance is
cosmologically redshifted by about . On the other hand, by assuming a cosmological model, e.g.
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 ...
, one can infer the Hubble constant from the size of the largest fluctuations seen 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 ...
. A higher Hubble constant would imply a smaller characteristic size of CMB fluctuations, and vice versa. The Planck collaboration measure the expansion rate this way and determine H
0 = . There is a disagreement between the two measurements, the distance ladder being model-independent and the CMB measurement depending on the fitted model, which hints at new physics beyond our standard cosmological models.
The Hubble parameter is not thought to be constant through time. There are dynamical forces acting on the particles in the universe that affect the expansion rate. It was earlier expected that the Hubble parameter would be decreasing as time went on due to the influence of gravitational interactions in the universe, and thus there is an additional observable quantity in the universe called the
deceleration parameter
The deceleration parameter ''q'' in cosmology is a dimensionless measure of the cosmic acceleration of the expansion of space in a Friedmann–Lemaître–Robertson–Walker universe. It is defined by:
:q \ \stackrel\ -\frac
where a is the s ...
, which cosmologists expected to be directly related to the matter density of the universe. Surprisingly, the deceleration parameter was measured by two different groups to be less than zero (actually, consistent with −1), which implied that today the Hubble parameter is converging to a constant value as time goes on. Some cosmologists have whimsically called the effect associated with the "accelerating universe" the "cosmic
jerk". The 2011
Nobel Prize in Physics
)
, image = Nobel Prize.png
, alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
was given for the discovery of this phenomenon.
In October 2018, scientists presented a new third way (two earlier methods, one based on
redshifts and another on the
cosmic distance ladder
The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects. A ''direct'' distance measurement of an astronomical object is possible o ...
, gave results that do not agree), using information from
gravitational wave events (especially those involving the
merger of neutron stars, like
GW170817
GW 170817 was a gravitational wave (GW) signal observed by the LIGO and Virgo detectors on 17 August 2017, originating from the shell elliptical galaxy . The signal was produced by the last minutes of a binary pair of neutron stars' insp ...
), of determining 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 ...
, essential in establishing the rate of expansion of the universe.
Measuring distances in expanding space
At cosmological scales, the present universe conforms to
Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean ...
, what cosmologists describe as ''geometrically flat'', to within experimental error.
Consequently, the rules of
Euclidean geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry: the '' Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms ...
associated with
Euclid's fifth postulate
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry:
''If a line segme ...
hold in the present universe in 3D space. It is, however, possible that the geometry of past 3D space could have been highly curved. The curvature of space is often modeled using a non-zero
Riemann curvature tensor
In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common way used to express the curvature of Riemannian manifolds. ...
in
Curvature of Riemannian manifolds
In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension greater than 2 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigoro ...
. Euclidean "geometrically flat" space has a
Riemann curvature tensor
In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common way used to express the curvature of Riemannian manifolds. ...
of zero.
"Geometrically flat" space has 3 dimensions and is consistent with Euclidean space. However,
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 differ ...
on the other hand, is 4 dimensions; it is not flat according to
Einsten's general theory of relativity. Einstein's theory postulates that "matter and energy curve spacetime, and there are enough matter and energy lying around to provide for curvature."
[What Do You Mean, The Universe Is Flat? (Part I)](_blank)
Scientific American, Davide Castelvecchi, July 25, 2011.
In part to accommodate such different geometries, the expansion of the universe is inherently
general relativistic. It cannot be modeled with
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws ...
alone: though
such models exist, they are at fundamental odds with the observed interaction between matter and spacetime seen in our universe.
The images to the right show two views of
spacetime diagrams that show the large-scale geometry of the universe according to the
ΛCDM
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 w ...
cosmological model. Two of the dimensions of space are omitted, leaving one dimension of space (the dimension that grows as the cone gets larger) and one of time (the dimension that proceeds "up" the cone's surface). The narrow circular end of the diagram corresponds to a
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 ...
of 700 million years after the Big Bang, while the wide end is a cosmological time of 18 billion years, where one can see the beginning of the
accelerating expansion as a splaying outward of the spacetime, a feature that eventually dominates in this model. The purple grid lines mark off cosmological time at intervals of one billion years from the Big Bang. The cyan grid lines mark off
comoving distance
In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects. ''Proper distance'' roughly corresponds to where a distant object would be at a spec ...
at intervals of one billion light years in the present era (less in the past and more in the future). Note that the circular curling of the surface is an artifact of the embedding with no physical significance and is done purely for illustrative purposes; a flat universe does not curl back onto itself. (A similar effect can be seen in the tubular shape of the
pseudosphere
In geometry, a pseudosphere is a surface with constant negative Gaussian curvature.
A pseudosphere of radius is a surface in \mathbb^3 having curvature in each point. Its name comes from the analogy with the sphere of radius , which is a surface ...
.)
The brown line on the diagram is the
worldline
The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept in modern physics, and particularly theoretical physics.
The concept of a "world line" is distinguished from con ...
of Earth (or more precisely its location in space, even before it was formed). The yellow line is the worldline of the most distant known
quasar. The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching Earth at the present day. The orange line shows the present-day distance between the quasar and Earth, about 28 billion light years, which is a larger distance than the age of the universe multiplied by the speed of light, ''ct''.
According to the
equivalence principle of general relativity, the rules of special relativity are ''locally'' valid in small regions of spacetime that are approximately flat. In particular, light always travels locally at the speed ''c''; in the diagram, this means, according to the convention of constructing spacetime diagrams, that light beams always make an angle of 45° with the local grid lines. It does not follow, however, that light travels a distance ''ct'' in a time ''t'', as the red worldline illustrates. While it always moves locally at ''c'', its time in transit (about 13 billion years) is not related to the distance traveled in any simple way, since the universe expands as the light beam traverses space and time. The distance traveled is thus inherently ambiguous because of the changing scale of the universe. Nevertheless, there are two distances that appear to be physically meaningful: the distance between Earth and the quasar when the light was emitted, and the distance between them in the present era (taking a slice of the cone along the dimension defined as the spatial dimension). The former distance is about 4 billion light years, much smaller than ''ct'', whereas the latter distance (shown by the orange line) is about 28 billion light years, much larger than ''ct''. In other words, if space were not expanding today, it would take 28 billion years for light to travel between Earth and the quasar, while if the expansion had stopped at the earlier time, it would have taken only 4 billion years.
The light took much longer than 4 billion years to reach us though it was emitted from only 4 billion light years away. In fact, the light emitted towards Earth was actually moving ''away'' from Earth when it was first emitted; the metric distance to Earth increased with cosmological time for the first few billion years of its travel time, also indicating that the expansion of space between Earth and the quasar at the early time was faster than the speed of light. None of this behavior originates from a special property of metric expansion, but rather from local principles of special relativity
integrated over a curved surface.
Topology of expanding space
![CMB Timeline300 no WMAP](https://upload.wikimedia.org/wikipedia/commons/6/6f/CMB_Timeline300_no_WMAP.jpg)
Over
time
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, ...
, the
space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually cons ...
that makes up the
universe
The universe 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 prevailing cosmological description of the development of the universe. ...
is expanding. The words '
space
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. In classical physics, physical space is often conceived in three linear dimensions, although modern physicists usually cons ...
' and '
universe
The universe 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 prevailing cosmological description of the development of the universe. ...
', sometimes used interchangeably, have distinct meanings in this context. Here 'space' is a mathematical concept that stands for the three-dimensional
manifold into which our respective positions are embedded while 'universe' refers to everything that exists including the matter and energy in space, the extra-dimensions that may be wrapped up in
various strings, and the time through which various events take place. The expansion of space is in reference to this 3-D manifold only; that is, the description involves no structures such as extra dimensions or an exterior universe.
The ultimate
topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
of space is ''
a posteriori'' – something that in principle must be observed – as there are no constraints that can simply be reasoned out (in other words there can not be any ''
a priori
("from the earlier") and ("from the later") are Latin phrases used in philosophy to distinguish types of knowledge, justification, or argument by their reliance on empirical evidence or experience. knowledge is independent from current ...
'' constraints) on how the space in which we live is
connected
Connected may refer to:
Film and television
* ''Connected'' (2008 film), a Hong Kong remake of the American movie ''Cellular''
* '' Connected: An Autoblogography About Love, Death & Technology'', a 2011 documentary film
* ''Connected'' (2015 TV ...
or whether it wraps around on itself as a
compact space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space by making precise the idea of a space having no "punctures" or "missing endpoints", ...
. Though certain cosmological models such as
Gödel's universe even permit bizarre
worldline
The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept in modern physics, and particularly theoretical physics.
The concept of a "world line" is distinguished from con ...
s that intersect with themselves, ultimately the question as to whether we are in something like a "
Pac-Man universe" where if traveling far enough in one direction would allow one to simply end up back in the same place like going all the way around the surface of a balloon (or a planet like the Earth) is
an observational question that is constrained as measurable or non-measurable by the universe's global geometry. At present, observations are consistent with the universe being infinite in extent and simply connected, though we are limited in distinguishing between simple and more complicated proposals by
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, the expanding universe, and the physics of Big Bang cosmology. Co ...
s. The universe could be infinite in extent or it could be finite; but the evidence that leads to the
inflationary model of the early universe also implies that the "total universe" is much larger than the
observable universe
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 ob ...
, and so any edges or exotic geometries or topologies would not be directly observable as light has not reached scales on which such aspects of the universe, if they exist, are still allowed. For all intents and purposes, it is safe to assume that the universe is infinite in spatial extent, without edge or strange connectedness.
Regardless of the overall shape of the universe, the question of what the universe is expanding into is one that does not require an answer according to the theories that describe the expansion; the way we define space in our universe in no way requires additional exterior space into which it can expand since an expansion of an infinite expanse can happen without changing the infinite extent of the expanse. All that is certain is that the manifold of space in which we live simply has the property that the distances between objects are getting larger as time goes on. This only implies the simple observational consequences associated with the metric expansion explored below. No "outside" or embedding in hyperspace is required for an expansion to occur. The visualizations often seen of the universe growing as a bubble into nothingness are misleading in that respect. There is no reason to believe there is anything "outside" of the expanding universe into which the universe expands.
Even if the overall spatial extent is infinite and thus the universe cannot get any "larger", we still say that space is expanding because, locally, the characteristic distance between objects is increasing. As an infinite space grows, it remains infinite.
Density of universe during expansion
Despite being extremely
dense
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...
when very young and during part of its early expansion - far denser than is usually required to form a
black hole - the universe did not re-collapse into a black hole. This is because commonly used calculations for
gravitational collapse are usually based upon objects of relatively constant size, such as
stars, and do not apply to rapidly expanding space such as the Big Bang.
Effects of expansion on small scales
The expansion of space is sometimes described as a force that acts to push objects apart. Though this is an accurate description of the effect of the
cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that Albert Einstein temporarily added to his field eq ...
, it is not an accurate picture of the phenomenon of expansion in general.
![Raisinbread](https://upload.wikimedia.org/wikipedia/commons/a/ac/Raisinbread.gif)
In addition to slowing the overall expansion, gravity causes local clumping of matter into stars and galaxies. Once objects are formed and bound by gravity, they "drop out" of the expansion and do not subsequently expand under the influence of the cosmological metric, there being no force compelling them to do so.
There is no difference between the inertial expansion of the universe and the inertial separation of nearby objects in a vacuum; the former is simply a large-scale extrapolation of the latter.
Once objects are bound by gravity, they no longer recede from each other. Thus, the Andromeda galaxy, which is bound to the Milky Way galaxy, is actually falling ''towards'' us and is not expanding away. Within the
Local Group
The Local Group is the galaxy group that includes the Milky Way.
It has a total diameter of roughly , and a total mass of the order of .
It consists of two collections of galaxies in a "dumbbell" shape: the Milky Way and its satellites form ...
, the gravitational interactions have changed the inertial patterns of objects such that there is no cosmological expansion taking place. Once one goes beyond the Local Group, the inertial expansion is measurable, though systematic gravitational effects imply that larger and larger parts of space will eventually fall out of the "
Hubble Flow
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 a ...
" and end up as bound, non-expanding objects up to the scales of
superclusters of galaxies. We can predict such future events by knowing the precise way the Hubble Flow is changing as well as the masses of the objects to which we are being gravitationally pulled. Currently, the Local Group is being gravitationally pulled towards either the
Shapley Supercluster or the "
Great Attractor
The Great Attractor is a gravitational anomaly in intergalactic space and the apparent central gravitational point of the Laniakea Supercluster. The observed anomalies suggest a localized concentration of mass millions of times more massive than ...
" with which, if dark energy were not acting, we would eventually merge and no longer see expand away from us after such a time.
A consequence of metric expansion being due to inertial motion is that a uniform local "explosion" of matter into a vacuum can be locally described by the
FLRW geometry, the same geometry that describes the expansion of the universe as a whole and was also the basis for the simpler
Milne universe
The Milne model was a special-relativistic cosmological model proposed by Edward Arthur Milne in 1935. It is mathematically equivalent to a special case of the FLRW model in the limit of zero energy density and it obeys the cosmological pri ...
, which ignores the effects of gravity. In particular, general relativity predicts that light will move at the speed ''c'' with respect to the local motion of the exploding matter, a phenomenon analogous to
frame dragging.
The situation changes somewhat with the introduction of dark energy or a cosmological constant. A cosmological constant due to a
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 ...
density has the effect of adding a repulsive force between objects that is proportional (not inversely proportional) to distance. Unlike inertia it actively "pulls" on objects that have clumped together under the influence of gravity, and even on individual atoms. However, this does not cause the objects to grow steadily or to disintegrate; unless they are very weakly bound, they will simply settle into an equilibrium state that is slightly (undetectably) larger than it would otherwise have been. As the universe expands and the matter in it thins, the gravitational attraction decreases (since it is proportional to the density), while the cosmological repulsion increases; thus the ultimate fate of the ΛCDM universe is a near vacuum expanding at an ever-increasing rate under the influence of the cosmological constant. However, the only locally visible effect of the
accelerating expansion is the disappearance (by runaway
redshift) of distant galaxies; gravitationally bound objects like the Milky Way do not expand and the Andromeda galaxy is moving fast enough towards us that it will still merge with the Milky Way in 3 billion years time, and it is also likely that the merged supergalaxy that forms will eventually fall in and merge with the nearby
Virgo Cluster
The Virgo Cluster is a large cluster of galaxies whose center is 53.8 ± 0.3 Mly (16.5 ± 0.1 Mpc) away in the constellation Virgo. Comprising approximately 1,300 (and possibly up to 2,000) member galaxies, the cluster forms the heart of the la ...
. However, galaxies lying farther away from this will recede away at ever-increasing speed and be redshifted out of our range of visibility.
Metric expansion and speed of light
At the end of the
early universe's inflationary period, all the matter and energy in the universe was set on an
inertial trajectory consistent with the
equivalence principle and
Einstein's general theory of relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...
and this is when the
precise and regular form of the universe's expansion had its origin (that is, matter in the universe is separating because it was separating in the past due to the
inflaton field).
While
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws ...
prohibits objects from moving faster than light with respect to a
local reference frame
In theoretical physics, a local reference frame (local frame) refers to a coordinate system or frame of reference that is only expected to function over a small region or a restricted region of space or spacetime.
The term is most often used in ...
where spacetime can be treated as
flat and unchanging, it does not apply to situations where
spacetime curvature
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. G ...
or evolution in time become important. These situations are described by
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 ...
, which allows the separation between two distant objects to increase faster than the speed of light, although the definition of "distance" here is somewhat different from that used in an inertial frame. The definition of distance used here is the summation or integration of local
comoving distance
In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects. ''Proper distance'' roughly corresponds to where a distant object would be at a spec ...
s, all done at constant local proper time. For example, galaxies that are farther than the
Hubble radius
In cosmology, a Hubble volume (named for the astronomer Edwin Hubble) or Hubble sphere, subluminal sphere, causal sphere and sphere of causality is a spherical region of the observable universe surrounding an observer beyond which objects recede ...
, approximately 4.5
gigaparsec
The parsec (symbol: pc) is a unit of length used to measure the large distances to astronomical objects outside the Solar System, approximately equal to or (au), i.e. . The parsec unit is obtained by the use of parallax and trigonometry, and ...
s or 14.7 billion
light-years, away from us have a recession speed that is faster than 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 ...
. Visibility of these objects depends on the exact expansion history of the universe. Light that is emitted today from galaxies beyond the more-distant
cosmological event horizon
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's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
, about 5 gigaparsecs or 16 billion light-years, will never reach us, although we can still see the light that these galaxies emitted in the past. Because of the high rate of expansion, it is also possible for a distance between two objects to be greater than the value calculated by multiplying the speed of light by the age of the universe. These details are a frequent source of confusion among amateurs and even professional physicists.
[Tamara M. Davis and Charles H. Lineweaver, ''Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe''. astro-ph/0310808] Due to the non-intuitive nature of the subject and what has been described by some as "careless" choices of wording, certain descriptions of the metric expansion of space and the misconceptions to which such descriptions can lead are an ongoing subject of discussion within the fields of
education
Education is a purposeful activity directed at achieving certain aims, such as transmitting knowledge or fostering skills and character traits. These aims may include the development of understanding, rationality, kindness, and honesty ...
and communication of scientific concepts.
Scale factor
At a fundamental level, the expansion of the universe is a property of spatial measurement on the largest measurable scales of our universe. The distances between cosmologically relevant points increases as time passes leading to observable effects outlined below. This feature of the universe can be characterized by a single parameter that is called the
scale factor
In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a '' scale factor'' that is the same in all directions. The result of uniform scaling is similar ...
, which is a
function
Function or functionality may refer to:
Computing
* Function key, a type of key on computer keyboards
* Function model, a structured representation of processes in a system
* Function object or functor or functionoid, a concept of object-oriente ...
of time and a single value for all of space at any instant (if the scale factor were a function of space, this would violate 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 ...
). By convention, the scale factor is set to be unity at the present time and, because the universe is expanding, is smaller in the past and larger in the future. Extrapolating back in time with certain cosmological models will yield a moment when the scale factor was zero; our current understanding of cosmology sets
this time at 13.799 ± 0.021 billion years ago. If the universe continues to expand forever, the scale factor will approach infinity in the future. In principle, there is no reason that the expansion of the universe must be
monotonic
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of ord ...
and there are models where at some time in the future the scale factor decreases with an attendant contraction of space rather than an expansion.
Other conceptual models of expansion
The expansion of space is often illustrated with conceptual models that show only the size of space at a particular time, leaving the dimension of time implicit.
In the "
ant on a rubber rope
The ant on a rubber rope is a mathematical puzzle with a solution that appears counterintuitive or paradoxical. It is sometimes given as a worm, or inchworm, on a rubber or elastic band, but the principles of the puzzle remain the same.
The det ...
model" one imagines an ant (idealized as pointlike) crawling at a constant speed on a perfectly elastic rope that is constantly stretching. If we stretch the rope in accordance with the ΛCDM scale factor and think of the ant's speed as the speed of light, then this analogy is numerically accurate – the ant's position over time will match the path of the red line on the embedding diagram above.
In the "rubber sheet model" one replaces the rope with a flat two-dimensional rubber sheet that expands uniformly in all directions. The addition of a second spatial dimension raises the possibility of showing local perturbations of the spatial geometry by local curvature in the sheet.
In the "balloon model" the flat sheet is replaced by a spherical balloon that is inflated from an initial size of zero (representing the big bang). A balloon has positive
Gaussian curvature while observations suggest that the real universe is spatially flat, but this inconsistency can be eliminated by making the balloon very large so that it is locally flat to within the limits of observation. This analogy is potentially confusing since it wrongly suggests that the big bang took place at the center of the balloon. In fact points off the surface of the balloon have no meaning, even if they were occupied by the balloon at an earlier time.
In the "raisin bread model" one imagines a loaf of raisin bread expanding in the oven. The loaf (space) expands as a whole, but the raisins (gravitationally bound objects) do not expand; they merely grow farther away from each other.
Theoretical basis and first evidence
Hubble's law
Technically, the metric expansion of space is a feature of many solutions to 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 ...
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 ...
, and distance is measured using the
Lorentz interval. This explains observations that indicate that
galaxies that are more distant from us are
receding faster than galaxies that are closer to us (see
Hubble's law
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 a ...
).
Cosmological constant and the Friedmann equations
The first general relativistic models predicted that a universe that was dynamical and contained ordinary gravitational matter would contract rather than expand. Einstein's first proposal for a solution to this problem involved adding a
cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that Albert Einstein temporarily added to his field eq ...
into his theories to balance out the contraction, in order to obtain a static universe solution. But in 1922
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 ...
derived a set of equations known as the
Friedmann equations
The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann ...
, showing that the universe might expand and presenting the expansion speed in this case. The observations of
Edwin Hubble in 1929 suggested that distant galaxies were all apparently moving away from us, so that many scientists came to accept that the universe was expanding.
Hubble's concerns over the rate of expansion
While the metric expansion of space appeared to be implied by Hubble's 1929 observations, Hubble disagreed with the expanding-universe interpretation of the data:
Hubble's skepticism about the universe being too small, dense, and young turned out to be based on an observational error. Later investigations appeared to show that Hubble had confused distant
H II region
An H II region or HII region is a region of interstellar atomic hydrogen that is ionized. It is typically in a molecular cloud of partially ionized gas in which star formation has recently taken place, with a size ranging from one to hundreds ...
s for
Cepheid variable
A Cepheid variable () is a type of star that pulsates radially, varying in both diameter and temperature and producing changes in brightness with a well-defined stable period and amplitude.
A strong direct relationship between a Cepheid vari ...
s and the Cepheid variables themselves had been inappropriately lumped together with low-luminosity
RR Lyrae
RR Lyrae is a variable star in the Lyra constellation, figuring in its west near to Cygnus. As the brightest star in its class, it became the eponym for the RR Lyrae variable class of stars and it has been extensively studied by astro ...
stars causing calibration errors that led to a value of 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 ...
of approximately 500
km/
s/
Mpc instead of the true value of approximately 70 km/s/Mpc. The higher value meant that an expanding universe would have an age of 2 billion years (younger than the
Age of the Earth) and extrapolating the observed number density of galaxies to a rapidly expanding universe implied a mass density that was too high by a similar factor, enough to force the universe into a peculiar
closed geometry that also implied an impending
Big Crunch that would occur on a similar timescale. After fixing these errors in the 1950s, the new lower values for the Hubble Constant accorded with the expectations of an older universe and the density parameter was found to be fairly close to a geometrically flat universe.
However, recent measurements of the distances and velocities of faraway galaxies revealed a 9 percent discrepancy in the value of the Hubble constant, implying a universe that seems expanding too fast compared to previous measurements.
In 2001, Wendy Freedman determined space to expand at 72 kilometers per second per megaparsec - roughly 3.3 million light years - meaning that for every 3.3 million light years further away from the earth you are, the matter where you are, is moving away from earth 72 kilometers a second faster.
In the summer of 2016, another measurement reported a value of 73 for the constant, thereby contradicting 2013 measurements from the European Planck mission of slower expansion value of 67. The discrepancy opened new questions concerning the nature of dark energy, or of neutrinos.
Inflation as an explanation for the expansion
Until the theoretical developments in the 1980s no one had an explanation for why this seemed to be the case, but with the development of models of
cosmic inflation, the expansion of the universe became a general feature resulting from
vacuum decay
In quantum field theory, a false vacuum is a hypothetical vacuum that is relatively stable, but not in the most stable state possible. This condition is known as metastable. It may last for a very long time in that state, but could eventually ...
. Accordingly, the question "why is the universe expanding?" is now answered by understanding the details of the inflation decay process that occurred in the first
10−32 seconds of the existence of our universe. During inflation, the metric changed
exponentially
Exponential may refer to any of several mathematical topics related to exponentiation, including:
*Exponential function, also:
**Matrix exponential, the matrix analogue to the above
*Exponential decay, decrease at a rate proportional to value
*Expo ...
, causing any volume of space that was smaller than an
atom
Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons.
Every solid, liquid, gas, ...
to grow to around 100 million
light years across in a time scale similar to the time when inflation occurred (10
−32 seconds).
Measuring distance in a metric space
![Space Expansion (no center)](https://upload.wikimedia.org/wikipedia/commons/c/c7/Space_Expansion_%28no_center%29.png)
In expanding space, distance is a dynamic quantity that changes with time. There are several different ways of defining distance in cosmology, known as ''distance measures'', but a common method used amongst modern astronomers is comoving distance.
The metric only defines the distance between nearby (so-called "local") points. In order to define the distance between arbitrarily distant points, one must specify both the points and a specific curve (known as a "
spacetime interval
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 ...
") connecting them. The distance between the points can then be found by finding the length of this connecting curve through the three dimensions of space. Comoving distance defines this connecting curve to be a curve of constant
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 ...
. Operationally, comoving distances cannot be directly measured by a single Earth-bound observer. To determine the distance of distant objects, astronomers generally measure luminosity of
standard candles, or the redshift factor 'z' of distant galaxies, and then convert these measurements into distances based on some particular model of spacetime, such as 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 ...
. It is, indeed, by making such observations that it was determined that there is no evidence for any 'slowing down' of the expansion in the current epoch.
Observational evidence
Theoretical cosmologists developing
models of the universe
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's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
have drawn upon a small number of reasonable assumptions in their work. These workings have led to models in which the metric expansion of space is a likely feature of the universe. Chief among the underlying principles that result in models including metric expansion as a feature are:
* 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 ...
that demands that the universe looks the same way in all directions (
isotropic) and has roughly the same smooth mixture of material (
homogeneous).
* the
Copernican Principle that demands that no place in the universe is preferred (that is, the universe has no "starting point").
Scientists have tested carefully whether these assumptions are valid and borne out by observation.
Observational cosmologists have discovered evidence – very strong in some cases – that supports these assumptions, and as a result, metric expansion of space is considered by cosmologists to be an observed feature on the basis that although we cannot see it directly, scientists have tested the properties of the universe and observation provides compelling confirmation. Sources of this confidence and confirmation include:
* Hubble demonstrated that all galaxies and distant astronomical objects were moving away from us, as predicted by a universal expansion. Using the
redshift of their
electromagnetic spectra to determine the distance and speed of remote objects in space, he showed that all objects are moving away from us, and that their speed is proportional to their distance, a feature of metric expansion. Further studies have since shown the expansion to be highly
isotropic and
homogeneous, that is, it does not seem to have a special point as a "center", but appears universal and independent of any fixed central point.
* In studies of
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 obj ...
taken from
redshift survey
In astronomy, a redshift survey is a survey of a section of the sky to measure the redshift of astronomical objects: usually galaxies, but sometimes other objects such as galaxy clusters or quasars.
Using Hubble's law, the redshift can be use ...
s a so-called "
End of Greatness
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 ob ...
" was discovered at the largest scales of the universe. Until these scales were surveyed, the universe appeared "lumpy" with clumps of
galaxy cluster
A galaxy cluster, or a cluster of galaxies, is a structure that consists of anywhere from hundreds to thousands of galaxies that are bound together by gravity, with typical masses ranging from 1014 to 1015 solar masses. They are the second-lar ...
s,
superclusters and
filaments that were anything but isotropic and homogeneous. This lumpiness disappears into a smooth distribution of galaxies at the largest scales.
* The isotropic distribution across the sky of distant
gamma-ray burst
In gamma-ray astronomy, gamma-ray bursts (GRBs) are immensely energetic explosions that have been observed in distant galaxies. They are the most energetic and luminous electromagnetic events since the Big Bang. Bursts can last from ten millise ...
s and
supernovae is another confirmation of the Cosmological Principle.
* The Copernican Principle was not truly tested on a cosmological scale until measurements of the effects of 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 ...
radiation on the dynamics of distant astrophysical systems were made. A group of astronomers at the
European Southern Observatory noticed, by measuring the temperature of a distant intergalactic cloud in thermal equilibrium with the cosmic microwave background, that the radiation from the Big Bang was demonstrably warmer at earlier times. Uniform cooling of the cosmic microwave background over billions of years is strong and direct observational evidence for metric expansion.
Taken together, these phenomena overwhelmingly support models that rely on space expanding through a change in metric. It was not until the discovery in the year 2000 of direct observational evidence for the changing temperature of the cosmic microwave background that more bizarre constructions could be ruled out. Until that time, it was based purely on an assumption that the universe did not behave as one with 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. ...
sitting at the middle of a fixed-metric with a universal explosion of galaxies in all directions (as seen in, for example, an
early model proposed by Milne). Yet before this evidence, many rejected the Milne viewpoint based on the
mediocrity principle
The mediocrity principle is the philosophical notion that "if an item is drawn at random from one of several sets or categories, it's more likely to come from the most numerous category than from any one of the less numerous categories". The prin ...
.
More direct results of the expansion, such as change of redshift, distance, flux, angular position and the angular size of astronomical objects, have not been detected yet due to smallness of these effects. Change of the redshift or the flux could be observed by
Square Kilometre Array
The Square Kilometre Array (SKA) is an intergovernmental international radio telescope project being built in Australia (low-frequency) and South Africa (mid-frequency). The combining infrastructure, the Square Kilometre Array Observatory (SKA ...
or
Extremely Large Telescope
The Extremely Large Telescope (ELT) is an astronomical observatory currently under construction. When completed, it is planned to be the world's largest optical/near-infrared extremely large telescope. Part of the European Southern Observatory ...
in the mid-2030s.
Direct detection of the cosmic expansion: the redshift drift and the flux drift
/ref>
See also
*Comoving and proper distances
In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects. ''Proper distance'' roughly corresponds to where a distant object would be at a spec ...
Notes
References
Printed references
* Eddington, Arthur. ''The Expanding Universe: Astronomy's 'Great Debate', 1900-1931''. Press Syndicate of the University of Cambridge, 1933.
* Liddle, Andrew R. and David H. Lyth. ''Cosmological Inflation and Large-Scale Structure''. Cambridge University Press, 2000.
* Lineweaver, Charles H. and Tamara M. Davis,
Misconceptions about the Big Bang
, ''Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it ...
'', March 2005 (non-free content).
* Mook, Delo E. and Thomas Vargish. ''Inside Relativity''. Princeton University Press, 1991.
External links
* Swenson, Ji
Answer to a question about the expanding universe
* Felder, Gary,
.
* NASA
The National Aeronautics and Space Administration (NASA ) is an independent agencies of the United States government, independent agency of the US federal government responsible for the civil List of government space agencies, space program ...
's WMAP
The Wilkinson Microwave Anisotropy Probe (WMAP), originally known as the Microwave Anisotropy Probe (MAP and Explorer 80), was a NASA spacecraft operating from 2001 to 2010 which measured temperature differences across the sky in the cosmic mic ...
team offers an
Explanation of the universal expansion
at a very elementary level
* ttps://web.archive.org/web/20130922085443/http://theory.uwinnipeg.ca/mod_tech/node216.html Expanding raisin breadfrom the University of Winnipeg: an illustration, but no explanation
"Ant on a balloon" analogy to explain the expanding universe
at "Ask an Astronomer". (The astronomer who provides this explanation is not specified.)
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