Expansion of the universe

A graphical representation of the expansion of the universe from the Big Bang to the present day, with the inflationary epoch represented as the dramatic expansion seen on the left. This visualization shows only a section of the universe; the empty space outside the diagram should not be taken to represent empty space outside the universe (which does not necessarily exist).

The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time. ^[1] It is an intrinsic expansion, so it does not mean that the universe expands "into" anything or that space exists "outside" it. To any observer in the universe, it appears that all but the nearest galaxies (which are bound to each other by gravity) move away at speeds that are proportional to their distance from the observer, on average. While objects cannot move faster than light, this limitation applies only with respect to local reference frames and does not limit the recession rates of cosmologically distant objects.

Cosmic expansion is a key feature of Big Bang cosmology. It can be modeled mathematically with the Friedmann–Lemaître–Robertson–Walker metric (FLRW), where it corresponds to an increase in the scale of the spatial part of the universe's spacetime metric tensor (which governs the size and geometry of spacetime). Within this framework, the separation of objects over time is associated with the expansion of space itself. However, this is not a generally covariant description but rather only a choice of coordinates. Contrary to common misconception, it is equally valid to adopt a description in which space does not expand and objects simply move apart while under the influence of their mutual gravity. ^{[2] [3] [4]} Although cosmic expansion is often framed as a consequence of general relativity, it is also predicted by Newtonian gravity. ^{[5] [6]}

According to inflation theory, the universe suddenly expanded during the inflationary epoch (about 10⁻³² of a second after the Big Bang), and its volume increased by a factor of at least 10⁷⁸ (an expansion of distance by a factor of at least 10²⁶ in each of the three dimensions). This would be equivalent to expanding an object 1  nanometer across (10⁻⁹ m, about half the width of a molecule of DNA) to one approximately 10.6  light-years across (about 10¹⁷ m, or 62 trillion miles). Cosmic expansion subsequently decelerated to much slower rates, until 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, appearing as a cosmological constant 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, this acceleration becomes dominant in the future.

History

In 1912–1914, Vesto Slipher discovered that light from remote galaxies was redshifted, ^{[7] [8]} a phenomenon later interpreted as galaxies receding from the Earth. In 1922, Alexander Friedmann used the Einstein field equations to provide theoretical evidence that the universe is expanding. ^[9]

Swedish astronomer Knut Lundmark 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." ^[10]

In 1927, Georges Lemaître 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. ^[11] Edwin Hubble observationally confirmed Lundmark's and Lemaître's findings in 1929. ^[12] Assuming the cosmological principle, these findings would imply that all galaxies are moving away from each other.

Astronomer Walter Baade recalculated the size of the known universe in the 1940s, doubling the previous calculation made by Hubble in 1929. ^{[13] [14] [15]} He announced this finding to considerable astonishment at the 1952 meeting of the International Astronomical Union in Rome. For most of the second half of the 20th century, the value of the Hubble constant was estimated to be between 50 and 90 km⋅s⁻¹⋅Mpc ⁻¹.

On 13 January 1994, NASA formally announced a completion of its repairs related to the main mirror of the Hubble Space Telescope, allowing for sharper images and, consequently, more accurate analyses of its observations. ^[16] Shortly 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 measurement of 80±17 km⋅s⁻¹⋅Mpc⁻¹. ^[17] Later the same year, Adam Riess et al. used an empirical method of visual-band light-curve shapes to more finely estimate the luminosity of Type Ia supernovae. This further minimized the systematic 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 calibrations of Type Ia supernova, which estimates a Hubble constant of 73±7 km⋅s⁻¹⋅Mpc⁻¹. ^[18] In 2003, David Spergel's analysis of the cosmic microwave background 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. ^[19]

Structure of cosmic expansion

The universe at the largest scales is observed to be homogeneous (the same everywhere) and isotropic (the same in all directions), consistent with the cosmological principle. These constraints demand that any expansion of the universe accord with Hubble's law, in which objects recede from each observer with velocities proportional to their positions with respect to that observer. That is, recession velocities ${\displaystyle {\vec {v}}}$ scale with (observer-centered) positions ${\displaystyle {\vec {x}}}$ according to

${\displaystyle {\vec {v}}=H{\vec {x}},}$

where the Hubble rate ${\displaystyle H}$ quantifies the rate of expansion. ${\displaystyle H}$ is a function of cosmic time.

Dynamics of cosmic expansion

The expansion history depends on the density of the universe. Ω on this graph corresponds to the ratio of the matter density to the critical density, for a matter-dominated universe. The "acceleration" curve shows the trajectory of the scale factor for a universe with dark energy.

Mathematically, the expansion of the universe is quantified by the scale factor, ${\displaystyle a}$, which is proportional to the average separation between objects, such as galaxies. The scale factor is a function of time and is conventionally set to be ${\displaystyle a=1}$ at the present time. Because the universe is expanding, ${\displaystyle a}$ 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 13.787 ± 0.020 billion years ago. If the universe continues to expand forever, the scale factor will approach infinity in the future. It is also possible in principle for the universe to stop expanding and begin to contract, which corresponds to the scale factor decreasing in time.

The scale factor ${\displaystyle a}$ is a parameter of the FLRW metric, and its time evolution is governed by the Friedmann equations. The second Friedmann equation,

${\displaystyle {\frac {\ddot {a}}{a}}=-{\frac {4\pi G}{3}}\left(\rho +{\frac {3p}{c^{2}}}\right)+{\frac {\Lambda c^{2}}{3}},}$

shows how the contents of the universe influence its expansion rate. Here, ${\displaystyle G}$ is the gravitational constant, ${\displaystyle \rho }$ is the energy density within the universe, ${\displaystyle p}$ is the pressure, ${\displaystyle c}$ is the speed of light, and ${\displaystyle \Lambda }$ is the cosmological constant. A positive energy density leads to deceleration of the expansion, ${\displaystyle {\ddot {a}}<0}$, and a positive pressure further decelerates expansion. On the other hand, sufficiently negative pressure with ${\displaystyle p<-\rho c^{2}/3}$ leads to accelerated expansion, and the cosmological constant also accelerates expansion. Nonrelativistic matter is essentially pressureless, with ${\displaystyle |p|\ll \rho c^{2}}$, while a gas of ultrarelativistic particles (such as a photon gas) has positive pressure ${\displaystyle p=\rho c^{2}/3}$. Negative-pressure fluids, like dark energy, are not experimentally confirmed, but the existence of dark energy is inferred from astronomical observations.

Distances in the expanding universe

Comoving coordinates

Main article: Comoving and proper distances

In an expanding universe, it is often useful to study the evolution of structure with the expansion of the universe factored out. This motivates the use of comoving coordinates, which are defined to grow proportionally with the scale factor. If an object is moving only with the Hubble flow of the expanding universe, with no other motion, then it remains stationary in comoving coordinates. The comoving coordinates are the spatial coordinates in the FLRW metric.

Shape of the universe

Main article: Shape of the universe

The universe is a four-dimensional spacetime, but within a universe that obeys the cosmological principle, there is a natural choice of three-dimensional spatial surface. These are the surfaces on which observers who are stationary in comoving coordinates agree on the age of the universe. In a universe governed by special relativity, such surfaces would be hyperboloids, because relativistic time dilation means that rapidly receding distant observers' clocks are slowed, so that spatial surfaces must bend "into the future" over long distances. However, within general relativity, the shape of these comoving synchronous spatial surfaces is affected by gravity. Current observations are consistent with these spatial surfaces being geometrically flat (so that, for example, the angles of a triangle add up to 180 degrees).

Cosmological horizons

Main article: Cosmological horizon

An expanding universe typically has a finite age. Light, and other particles, can have propagated only a finite distance. The comoving distance that such particles can have covered over the age of the universe is known as the particle horizon, and the region of the universe that lies within our particle horizon is known as the observable universe.

If the dark energy that is inferred to dominate the universe today is a cosmological constant, then the particle horizon converges to a finite value in the infinite future. This implies that the amount of the universe that we will ever be able to observe is limited. Many systems exist whose light can never reach us, because there is a cosmic event horizon induced by the repulsive gravity of the dark energy.

Within the study of the evolution of structure within the universe, a natural scale emerges, known as the Hubble horizon. Cosmological perturbations much larger than the Hubble horizon are not dynamical, because gravitational influences do not have time to propagate across them, while perturbations much smaller than the Hubble horizon are straightforwardly governed by Newtonian gravitational dynamics.

Consequences of cosmic expansion

Velocities and redshifts

An object's peculiar velocity is its velocity with respect to the comoving coordinate grid, i.e., with respect to the average expansion-associated motion of the surrounding material. It is a measure of how a particle's motion deviates from the Hubble flow of the expanding universe. The peculiar velocities of nonrelativistic particles decay as the universe expands, in inverse proportion with the cosmic scale factor. This can be understood as a self-sorting effect. A particle that is moving in some direction gradually overtakes the Hubble flow of cosmic expansion in that direction, asymptotically approaching material with the same velocity as its own.

More generally, the peculiar momenta of both relativistic and nonrelativistic particles decay in inverse proportion with the scale factor. For photons, this leads to the cosmological redshift. While the cosmological redshift is often explained as the stretching of photon wavelengths due to "expansion of space", it is more naturally viewed as a consequence of the Doppler effect. ^[3]

Superluminal expansion

Special relativity is valid in all local inertial frames; analysis at the global level requires summation or integration of local comoving distances, all done at constant local proper time. ^[20] Special relativity prohibits objects from moving faster than light with respect to a local reference frame, but cosmological observations require general relativity. ^[20] In general relativity, relative relative velocity depends on time. For example, one might define the velocity of a distant galaxy as its velocity at the time a photon was emitted relative to observation at the present time, or its velocity when the photon is measured. ^[21] For example, galaxies that are farther than the Hubble radius, approximately 4.5  gigaparsecs or 14.7 billion light-years, away from us have a recession speed that is faster than the speed of light. 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, 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. ^[20] 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 and communication of scientific concepts. ^{[22] [23] [24]}

Temperature

The universe cools as it expands. This follows from the decay of particles' peculiar momenta, as discussed above. It can also be understood as adiabatic cooling. The temperature of ultrarelativistic fluids, often called "radiation" and including the cosmic microwave background, scales inversely with the scale factor (i.e. ${\displaystyle T\propto a^{-1}}$). The temperature of nonrelativistic matter drops more sharply, scaling as the inverse square of the scale factor (i.e. ${\displaystyle T\propto a^{-2}}$).

Density

The contents of the universe dilute as it expands. The number of particles within a comoving volume remains fixed (on average), while the volume expands. For nonrelativistic matter, this implies that the energy density drops as ${\displaystyle \rho \propto a^{-3}}$, where ${\displaystyle a}$ is the scale factor.

For ultrarelativistic particles ("radiation"), the energy density drops more sharply, as ${\displaystyle \rho \propto a^{-4}}$. This is because in addition to the volume dilution of the particle count, the energy of each particle (including the rest mass energy) also drops significantly due to the decay of peculiar momenta.

In general, we can consider a perfect fluid with pressure ${\displaystyle p=w\rho }$, where ${\displaystyle \rho }$ is the energy density. The parameter ${\displaystyle w}$ is the equation of state parameter. The energy density of such a fluid drops as

${\displaystyle \rho \propto a^{-3(1+w)}.}$

Nonrelativistic matter has ${\displaystyle w=0}$ while radiation has ${\displaystyle w=1/3}$. For an exotic fluid with negative pressure, like dark energy, the energy density drops more slowly; if ${\displaystyle w=-1}$ it remains constant in time. If ${\displaystyle w<-1}$, corresponding to phantom energy, the energy density grows as the universe expands.

Expansion history

Cosmic inflation

Main articles: inflation (cosmology) and inflaton

Inflation is a period of accelerated expansion hypothesized to have occurred at a time of around 10⁻³² seconds. It would have been driven by the inflaton, a field that has a positive-energy false vacuum state. Inflation was originally proposed to explain the absence of exotic relics predicted by grand unified theories, such as magnetic monopoles, because the rapid expansion would have diluted such relics. It was subsequently realized that the accelerated expansion would also solve the horizon problem and the flatness problem. Additionally, quantum fluctuations during inflation would have created initial variations in the density of the universe, which gravity later amplified to yield the observed spectrum of matter density variations.^{[ citation needed ]}

During inflation, the cosmic scale factor grew exponentially in time. In order to solve the horizon and flatness problems, inflation must have lasted long enough that the scale factor grew by at least a factor of e⁶⁰ (about 10²⁶). ^{[ citation needed ]}

Radiation epoch

The history of the universe after inflation but before a time of about 1 second is largely unknown. ^[25] However, the universe is known to have been dominated by ultrarelativistic Standard Model particles, conventionally called radiation, by the time of neutrino decoupling at about 1 second. ^[26] During radiation domination, cosmic expansion decelerated, with the scale factor growing proportionally with the square root of the time.

Matter epoch

Since radiation redshifts as the universe expands, eventually nonrelativistic matter came to dominate the energy density of the universe. This transition happened at a time of about 50 thousand years after the Big Bang. During the matter-dominated epoch, cosmic expansion also decelerated, with the scale factor growing as the 2/3 power of the time (${\displaystyle a\propto t^{2/3}}$). Also, gravitational structure formation is most efficient when nonrelativistic matter dominates, and this epoch is responsible for the formation of galaxies and the large-scale structure of the universe.

Dark energy

Main article: Dark energy

Around 3 billion years ago, at a time of about 11 billion years, dark energy is believed to have begun to dominate the energy density of the universe. This transition came about because dark energy does not dilute as the universe expands, instead maintaining a constant energy density. Similarly to inflation, dark energy drives accelerated expansion, such that the scale factor grows exponentially in time.

Measuring the expansion rate

When an object is receding, its light gets stretched (redshifted). When the object is approaching, its light gets compressed (blueshifted).

The most direct way to measure the expansion rate is to independently measure the recession velocities and the distances of distant objects, such as galaxies. The ratio between these quantities gives the Hubble rate, in accordance with Hubble's law. Typically, the distance is measured using a standard candle, which is an object or event for which the intrinsic brightness is known. The object's distance can then be inferred from the observed apparent brightness. Meanwhile, the recession speed is measured through the redshift. Hubble used this approach for his original measurement of the expansion rate, by measuring the brightness of Cepheid variable stars and the redshifts of their host galaxies. More recently, using Type Ia supernovae, the expansion rate was measured to be H₀ = 73.24±1.74 (km/s)/Mpc. ^[27] This means that for every million parsecs of distance from the observer, recessional velocity of objects at that distance increases by about 73 kilometres per second (160,000 mph).

Supernovae are observable at such great distances that the light travel time therefrom can approach the age of the universe. Consequently, they can be used to measure not only the present-day expansion rate but also the expansion history. In work that was awarded the 2011 Nobel Prize in Physics, supernova observations were used to determine that cosmic expansion is accelerating in the present epoch. ^[28]

By assuming a cosmological model, e.g. the Lambda-CDM model, another possibility is to infer the present-day expansion rate from the sizes of the largest fluctuations seen in the cosmic microwave background. A higher expansion rate would imply a smaller characteristic size of CMB fluctuations, and vice versa. The Planck collaboration measured the expansion rate this way and determined H₀ = 67.4±0.5 (km/s)/Mpc. ^[29] There is a disagreement between this measurement and the supernova-based measurements, known as the Hubble tension.

A third option proposed recently is to use information from gravitational wave events (especially those involving the merger of neutron stars, like GW170817), to measure the expansion rate. ^{[30] [31]} Such measurements do not yet have the precision to resolve the Hubble tension.

In principle, the cosmic expansion history can also be measured by studying how redshifts, distances, fluxes, angular positions, and angular sizes of astronomical objects change over the course of the time that they are being observed. These effects are too small to have yet been detected. However, changes in redshift or flux could be observed by the Square Kilometre Array or Extremely Large Telescope in the mid-2030s. ^[32]

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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 Lyth, David H. Cosmological Inflation and Large-Scale Structure. Cambridge University Press, 2000.
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• Mook, Delo E. and Thomas Vargish. Inside Relativity. Princeton University Press, 1991.

External links

• Swenson, Jim, Answer to a question about the expanding universe Archived 11 January 2009 at the Wayback Machine
• Felder, Gary, "The Expanding universe".
• NASA's WMAP team offers an "Explanation of the universal expansion" at an elementary level.
• Hubble Tutorial from the University of Wisconsin Physics Department Archived 9 June 2014 at the Wayback Machine
• Expanding raisin bread from 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).