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) recede 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, during the inflationary epoch about 10⁻³² of a second after the Big Bang, the universe suddenly expanded, 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 (10⁻⁹ m, about half the width of a molecule of DNA) in length to one approximately 10.6 light-years (about 10¹⁷ m, or 62 trillion miles) long. 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 more dominant into the future.

History

In 1912-14, Vesto M. 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 (Megaparsec).

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] 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 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 1a supernovae, 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 of the universe can be understood as a consequence of an initial impulse (possibly due to inflation), which sent the contents of the universe flying apart. The mutual gravitational attraction of the matter and radiation within the universe gradually slows this expansion over time, but expansion nevertheless continues due to momentum left over from the initial impulse. Also, certain exotic relativistic fluids, such as dark energy and inflation, exert gravitational repulsion in the cosmological context, which accelerates the expansion of the universe. A cosmological constant also has this effect.

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

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

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

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.

When studying 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 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]

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

${\displaystyle \mathrm{\rho <!--\; \rho \; -->}\propto <!--\; \propto \; -->a^{-<!--\; -\; -->3(1+w)}.}$Zdroj:https://en.wikipedia.org?pojem=Metric_expansion_of_space
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