# Observable universe

Visualization of the 93 billion light year – or 28 billion parsec – three-dimensional observable universe. The scale is such that the fine grains represent collections of large numbers of superclusters. The Virgo Supercluster – home of Milky Way – is marked at the center, but is too small to be seen in the image.

In Big Bang cosmology, the observable universe consists of the galaxies and other matter that can, in principle, be observed from Earth in the present day—because light (or other signals) from those objects has had time to reach the Earth since the beginning of the cosmological expansion. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction. That is, the observable universe is a spherical volume (a ball) centered on the observer, regardless of the shape of the universe as a whole. Every location in the universe has its own observable universe, which may or may not overlap with the one centered on Earth.

The word observable used in this sense does not depend on whether modern technology actually permits detection of radiation from an object in this region (or indeed on whether there is any radiation to detect). It simply indicates that it is possible in principle for light or other signals from the object to reach an observer on Earth. In practice, we can see light only from as far back as the time of photon decoupling in the recombination epoch. That is when particles were first able to emit photons that were not quickly re-absorbed by other particles. Before then, the universe was filled with a plasma that was opaque to photons.

The surface of last scattering is the collection of points in space at the exact distance that photons from the time of photon decoupling just reach us today. These are the photons we detect today as cosmic microwave background radiation (CMBR). However, it may be possible in the future to observe the still older neutrino background, or even more distant events via gravitational waves (which also should move at the speed of light). Sometimes astrophysicists distinguish between the visible universe, which includes only signals emitted since recombination—and the observable universe, which includes signals since the beginning of the cosmological expansion (the Big Bang in traditional cosmology, the end of the inflationary epoch in modern cosmology). According to calculations, the comoving distance (current proper distance) to particles from the CMBR, which represent the radius of the visible universe, is about 14.0 billion parsecs (about 45.7 billion light years), while the comoving distance to the edge of the observable universe is about 14.3 billion parsecs (about 46.6 billion light years),[1] about 2% larger.

The best estimate of the age of the universe as of 2013 is 13.798 ± 0.037 billion years[2] but due to the expansion of space humans are observing objects that were originally much closer but are now considerably farther away (as defined in terms of cosmological proper distance, which is equal to the comoving distance at the present time) than a static 13.8 billion light-years distance.[3] The diameter of the observable universe is estimated at about 28 billion parsecs (93 billion light-years),[4] putting the edge of the observable universe at about 46–47 billion light-years away.[5][6]

## The universe versus the observable universe

Some parts of the universe may simply be too far away for the light emitted from there at any moment since the Big Bang to have had enough time to reach Earth at present, so these portions of the universe would currently lie outside the observable universe. In the future the light from distant galaxies will have had more time to travel, so some regions not currently observable will become observable in the future. However, due to Hubble's law regions sufficiently distant from us are expanding away from us much faster than the speed of light (special relativity prevents nearby objects in the same local region from moving faster than the speed of light with respect to each other, but there is no such constraint for distant objects when the space between them is expanding; see uses of the proper distance for a discussion), and the expansion rate appears to be accelerating due to dark energy. Assuming dark energy remains constant (an unchanging cosmological constant), so that the expansion rate of the universe continues to accelerate, there is a "future visibility limit" beyond which objects will never enter our observable universe at any time in the infinite future, because light emitted by objects outside that limit would never reach us. (A subtlety is that, because the Hubble parameter is decreasing with time, there can be cases where a galaxy that is receding from us just a bit faster than light does emit a signal that reaches us eventually[6][7]). This future visibility limit is calculated at a comoving distance of 19 billion parsecs (62 billion light years) assuming the universe will keep expanding forever, which implies the number of galaxies that we can ever theoretically observe in the infinite future (leaving aside the issue that some may be impossible to observe in practice due to redshift, as discussed in the following paragraph) is only larger than the number currently observable by a factor of 2.36.[1]

Though in principle more galaxies will become observable in the future, in practice an increasing number of galaxies will become extremely redshifted due to ongoing expansion, so much so that they will seem to disappear from view and become invisible.[8][9][10] An additional subtlety is that a galaxy at a given comoving distance is defined to lie within the "observable universe" if we can receive signals emitted by the galaxy at any age in its past history (say, a signal sent from the galaxy only 500 million years after the Big Bang), but because of the universe's expansion, there may be some later age at which a signal sent from the same galaxy can never reach us at any point in the infinite future (so for example we might never see what the galaxy looked like 10 billion years after the Big Bang),[11] even though it remains at the same comoving distance (comoving distance is defined to be constant with time—unlike proper distance, which is used to define recession velocity due to the expansion of space), which is less than the comoving radius of the observable universe. This fact can be used to define a type of cosmic event horizon whose distance from us changes over time. For example, the current distance to this horizon is about 16 billion light years, meaning that a signal from an event happening at present can eventually reach us in the future if the event is less than 16 billion light years away, but the signal will never reach us if the event is more than 16 billion light years away.[6]

Both popular and professional research articles in cosmology often use the term "universe" to mean "observable universe". This can be justified on the grounds that we can never know anything by direct experimentation about any part of the universe that is causally disconnected from us, although many credible theories require a total universe much larger than the observable universe. No evidence exists to suggest that the boundary of the observable universe constitutes a boundary on the universe as a whole, nor do any of the mainstream cosmological models propose that the universe has any physical boundary in the first place, though some models propose it could be finite but unbounded, like a higher-dimensional analogue of the 2D surface of a sphere that is finite in area but has no edge. It is plausible that the galaxies within our observable universe represent only a minuscule fraction of the galaxies in the universe. According to the theory of cosmic inflation and its founder, Alan Guth, if it is assumed that inflation began about 10−37 seconds after the Big Bang, then with the plausible assumption that the size of the universe at this time was approximately equal to the speed of light times its age, that would suggest that at present the entire universe's size is at least 1023 times larger than the size of the observable universe.[12]

If the universe is finite but unbounded, it is also possible that the universe is smaller than the observable universe. In this case, what we take to be very distant galaxies may actually be duplicate images of nearby galaxies, formed by light that has circumnavigated the universe. It is difficult to test this hypothesis experimentally because different images of a galaxy would show different eras in its history, and consequently might appear quite different. Bielewicz et al.:[13] claims to establish a lower bound of 27.9 gigaparsecs (91 billion light-years) on the diameter of the last scattering surface (since this is only a lower bound, the paper leaves open the possibility that the whole universe is much larger, even infinite). This value is based on matching-circle analysis of the WMAP 7 year data. This approach has been disputed.[14]

## Size

The comoving distance from Earth to the edge of the observable universe is about 14 gigaparsecs (46 billion light years or 4.3×1026 meters) in any direction. The observable universe is thus a sphere with a diameter of about 29 gigaparsecs[15] (93 Gly or 8.8×1026 m).[16] Assuming that space is roughly flat, this size corresponds to a comoving volume of about 1.3×104 Gpc3 (4.1×105 Gly3 or 3.5×1080 m3).

The figures quoted above are distances now (in cosmological time), not distances at the time the light was emitted. For example, the cosmic microwave background radiation that we see right now was emitted at the time of photon decoupling, estimated to have occurred about 380,000 years after the Big Bang,[17][18] which occurred around 13.8 billion years ago. This radiation was emitted by matter that has, in the intervening time, mostly condensed into galaxies, and those galaxies are now calculated to be about 46 billion light-years from us.[1][6] To estimate the distance to that matter at the time the light was emitted, we may first note that according to the Friedmann–Lemaître–Robertson–Walker metric, which is used to model the expanding universe, if at the present time we receive light with a redshift of z, then the scale factor at the time the light was originally emitted is given by the following equation.[19][20]

$\! a(t) = \frac{1}{1 + z}$

WMAP nine-year results give the redshift of photon decoupling as z=1091.64  ± 0.47[17] which implies that the scale factor at the time of photon decoupling would be 11092.64. So if the matter that originally emitted the oldest CMBR photons has a present distance of 46 billion light years, then at the time of decoupling when the photons were originally emitted, the distance would have been only about 42 million light-years away.

### Misconceptions

Many secondary sources have reported a wide variety of incorrect figures for the size of the visible universe. Some of these figures are listed below, with brief descriptions of possible reasons for misconceptions about them.

13.8 billion light-years
The age of the universe is estimated to be 13.8 billion years. While it is commonly understood that nothing can accelerate to velocities equal to or greater than that of light, it is a common misconception that the radius of the observable universe must therefore amount to only 13.8 billion light-years. This reasoning makes sense only if the universe is the flat, static Minkowski spacetime of special relativity, but in the real universe, spacetime is curved in a way that corresponds to the expansion of space, as evidenced by Hubble's law. Distances obtained as the speed of light multiplied by a cosmological time interval have no direct physical significance.[21]
An example of one of the most common misconceptions about the size of the observable universe. Despite the fact that the universe is 13.8 billion years old, the distance to the edge of the observable universe is not 13.8 billion light-years, because the universe is expanding. This plaque appears at the Rose Center for Earth and Space in New York City.
15.8 billion light-years
This is obtained in the same way as the 13.8 billion light year figure, but starting from an incorrect age of the universe that the popular press reported in mid-2006.[22][23][24] For an analysis of this claim and the paper that prompted it, see the following reference at the end of this article.[25]
27.6 billion light-years
This is a diameter obtained from the (incorrect) radius of 13.8 billion light-years.
78 billion light-years
In 2003, Cornish et al.[26] found this lower bound for the diameter of the whole universe (not just the observable part), if we postulate that the universe is finite in size due to its having a nontrivial topology,[27][28] with this lower bound based on the estimated current distance between points that we can see on opposite sides of the cosmic microwave background radiation (CMBR). If the whole universe is smaller than this sphere, then light has had time to circumnavigate it since the big bang, producing multiple images of distant points in the CMBR, which would show up as patterns of repeating circles.[29] Cornish et al. looked for such an effect at scales of up to 24 gigaparsecs (78 Gly or 7.4×1026 m) and failed to find it, and suggested that if they could extend their search to all possible orientations, they would then "be able to exclude the possibility that we live in a universe smaller than 24 Gpc in diameter". The authors also estimated that with "lower noise and higher resolution CMB maps (from WMAP's extended mission and from Planck), we will be able to search for smaller circles and extend the limit to ~28 Gpc."[26] This estimate of the maximum lower bound that can be established by future observations corresponds to a radius of 14 gigaparsecs, or around 46 billion light years, about the same as the figure for the radius of the visible universe (whose radius is defined by the CMBR sphere) given in the opening section. A 2012 preprint by most of the same authors as the Cornish et al. paper has extended the current lower bound to a diameter of 98.5% the diameter of the CMBR sphere, or about 26 Gpc.[30]
156 billion light-years
This figure was obtained by doubling 78 billion light-years on the assumption that it is a radius.[31] Since 78 billion light-years is already a diameter (the original paper by Cornish et al. says, "By extending the search to all possible orientations, we will be able to exclude the possibility that we live in a universe smaller than 24 Gpc in diameter," and 24 Gpc is 78 billion light years),[26] the doubled figure is incorrect. This figure was very widely reported.[31][32][33] A press release from Montana State University – Bozeman, where Cornish works as an astrophysicist, noted the error when discussing a story that had appeared in Discover magazine, saying "Discover mistakenly reported that the universe was 156 billion light-years wide, thinking that 78 billion was the radius of the universe instead of its diameter."[34]
180 billion light-years
This estimate accompanied the age estimate of 15.8 billion years in some sources;[35] it was obtained by adding 15% to the figure of 156 billion light years.

## Large-scale structure

Sky surveys and mappings of the various wavelength bands of electromagnetic radiation (in particular 21-cm emission) have yielded much information on the content and character of the universe's structure. The organization of structure appears to follow as a hierarchical model with organization up to the scale of superclusters and filaments. Larger than this, there seems to be no continued structure, a phenomenon that has been referred to as the End of Greatness.

### Walls, filaments, and voids

The organization of structure arguably begins at the stellar level, though most cosmologists rarely address astrophysics on that scale. Stars are organized into galaxies, which in turn form clusters of galaxies and superclusters that are separated by immense voids, creating a vast foam-like structure sometimes called the "cosmic web". Prior to 1989, it was commonly assumed that virialized galaxy clusters were the largest structures in existence, and that they were distributed more or less uniformly throughout the universe in every direction. However, based on redshift survey data, in 1989 Margaret Geller and John Huchra discovered the "Great Wall",[36] a sheet of galaxies more than 500 million light-years long and 200 million wide, but only 15 million light-years thick. The existence of this structure escaped notice for so long because it requires locating the position of galaxies in three dimensions, which involves combining location information about the galaxies with distance information from redshifts. In April 2003, another large-scale structure was discovered, the Sloan Great Wall. In August 2007, a possible supervoid was detected in the constellation Eridanus.[37] It coincides with the 'WMAP Cold Spot', a cold region in the microwave sky that is highly improbable under the currently favored cosmological model. This supervoid could cause the cold spot, but to do so it would have to be improbably big, possibly a billion light-years across.

Another large-scale structure is the Newfound Blob, a collection of galaxies and enormous gas bubbles that measures about 200 million light years across.

In recent studies the universe appears as a collection of giant bubble-like voids separated by sheets and filaments of galaxies, with the superclusters appearing as occasional relatively dense nodes. This network is clearly visible in the 2dF Galaxy Redshift Survey. In the figure, a three dimensional reconstruction of the inner parts of the survey is shown, revealing an impressive view of the cosmic structures in the nearby universe. Several superclusters stand out, such as the Sloan Great Wall, the largest wall known to date.

On January 11, 2013, a large quasar group, the Huge-LQG, was discovered, which was measured to be four billion light-years across, the largest known structure in the universe.[38]

### End of Greatness

The End of Greatness is an observational scale discovered at roughly 100 Mpc (roughly 300 million lightyears) where the lumpiness seen in the large-scale structure of the universe is homogenized and isotropized in accordance with the Cosmological Principle. At this scale, no pseudo-random fractalness is apparent.[39] The superclusters and filaments seen in smaller surveys are randomized to the extent that the smooth distribution of the universe is visually apparent. It was not until the redshift surveys of the 1990s were completed that this scale could accurately be observed.[40]

### Observations

"Panoramic view of the entire near-infrared sky reveals the distribution of galaxies beyond the Milky Way. The image is derived from the 2MASS Extended Source Catalog (XSC)—more than 1.5 million galaxies, and the Point Source Catalog (PSC)--nearly 0.5 billion Milky Way stars. The galaxies are color-coded by 'redshift' obtained from the UGC, CfA, Tully NBGC, LCRS, 2dF, 6dFGS, and SDSS surveys (and from various observations compiled by the NASA Extragalactic Database), or photo-metrically deduced from the K band (2.2 um). Blue are the nearest sources (z < 0.01); green are at moderate distances (0.01 < z < 0.04) and red are the most distant sources that 2MASS resolves (0.04 < z < 0.1). The map is projected with an equal area Aitoff in the Galactic system (Milky Way at center)." [41]

Another indicator of large-scale structure is the 'Lyman alpha forest'. This is a collection of absorption lines that appear in the spectral lines of light from quasars, which are interpreted as indicating the existence of huge thin sheets of intergalactic (mostly hydrogen) gas. These sheets appear to be associated with the formation of new galaxies.

Caution is required in describing structures on a cosmic scale because things are often different than they appear. Bending of light by gravitation (gravitational lensing) can make images appear to originate in a different direction from their real source. This is caused when foreground objects (such as galaxies) curve surrounding spacetime (as predicted by general relativity), and deflect passing light rays. Rather usefully, strong gravitational lensing can sometimes magnify distant galaxies, making them easier to detect. Weak lensing (gravitational shear) by the intervening universe in general also subtly changes the observed large-scale structure. In 2004, measurements of this subtle shear show considerable promise as a test of cosmological models.

The large-scale structure of the universe also looks different if one only uses redshift to measure distances to galaxies. For example, galaxies behind a galaxy cluster are attracted to it, and so fall towards it, and so are slightly blueshifted (compared to how they would be if there were no cluster) On the near side, things are slightly redshifted. Thus, the environment of the cluster looks a bit squashed if using redshifts to measure distance. An opposite effect works on the galaxies already within the cluster: the galaxies have some random motion around the cluster centre, and when these random motions are converted to redshifts, the cluster appears elongated. This creates finger of God—the illusion of a long chain of galaxies pointed at the Earth.

### Cosmography of our cosmic neighborhood

At the centre of the Hydra-Centaurus Supercluster, a gravitational anomaly called the Great Attractor affects the motion of galaxies over a region hundreds of millions of light-years across. These galaxies are all redshifted, in accordance with Hubble's law. This indicates that they are receding from us and from each other, but the variations in their redshift are sufficient to reveal the existence of a concentration of mass equivalent to tens of thousands of galaxies.

The Great Attractor, discovered in 1986, lies at a distance of between 150 million and 250 million light-years (250 million is the most recent estimate), in the direction of the Hydra and Centaurus constellations. In its vicinity there is a preponderance of large old galaxies, many of which are colliding with their neighbours, and/or radiating large amounts of radio waves.

In 1987 Astronomer R. Brent Tully of the University of Hawaii’s Institute of Astronomy identified what he called the Pisces-Cetus Supercluster Complex, a structure one billion light years long and 150 million light years across in which, he claimed, the Local Supercluster was embedded.[42][43]

## Matter content

The observable universe contains between 1022 and 1024 stars (between 10 sextillion and 1 septillion stars).[44][45][46][47] To be slightly more precise, according to the Sloan Digital Sky Survey, "[by] a conservative estimate.... the currently observable universe is home to of order 6 x 1022 stars"[1] These stars are organized in more than 100 to 200 billion (up to 1 trillion depending on sources) galaxies, which themselves form groups, clusters, superclusters, sheets, filaments, and walls.[48]

Two approximate calculations give the number of atoms in the observable universe to be close to 1080.

### Method 1

Observations of the cosmic microwave background from the Wilkinson Microwave Anisotropy Probe suggest that the spatial curvature of the universe is very close to zero, which in current cosmological models implies that the value of the density parameter must be very close to a certain critical value. A NASA page gives this density, which includes dark energy, dark matter and ordinary matter all lumped together, as 9.9×10−27 kg/m3,[49] although the figure has not been updated since 2005[50] and a number of new estimates of the Hubble parameter have been made since then. The present value of the Hubble parameter $H_0$ is important because it is related to the value of the critical density at the present, $\rho_c$, by the equation[51]

$\rho_c = \frac{3H_0^2}{8 \pi G}$

where G is the gravitational constant. WMAP seven-year results from 2010 estimate the value of the $H_0$ at 70.4 (km/s)/Mpc[17] or 2.28×10−18 s−1, which gives a critical density of 9.30×10−27 kg/m3.

### Method 2

A typical star has a mass of about 2×1030 kg, which is about 1×1057 atoms of hydrogen per star. A typical galaxy has about 400 billion stars so that means each galaxy has 1×1057 × 4×1011 = 4×1068 hydrogen atoms. There are possibly 80 billion galaxies in the universe, so that means that there are about 4×1068 × 8×1010 = 3×1079 hydrogen atoms in the observable universe. But this is definitely a lower limit calculation, and it ignores many possible atom sources such as intergalactic gas.[52]

## Mass

Some care is required in defining what is meant by the total mass of the observable universe. In relativity, mass and energy are equivalent, and energy can take on a variety of forms, including energy that is associated with the curvature of spacetime itself, not with its contents such as atoms and photons. Defining the total energy of a large region of curved spacetime is problematic because there is no single agreed-upon way to define the energy due to gravity (the energy associated with spacetime curvature); for example, when photons are redshifted due to the expansion of the universe, they lose energy, and some physicists would say the energy has been converted to gravitational energy while others would say the energy has simply been lost.[53] One can, however, derive an order-of-magnitude estimate of the mass due to sources other than gravity, namely visible matter, dark matter and dark energy, based on the volume of the observable universe and the mean density.[54]

### Estimation based on critical density

As noted in the previous section, since the universe seems to be close to spatially flat, this suggests the density is close to the critical density, estimated above at 9.30×10−27 kg/m3. Multiplying this by (A) the estimated volume of the visible universe (3.38×1080 m3) gives a total mass for the visible universe of 3.14×1054 kg, while multiplying by (B) the estimated volume of the observable universe (3.60×1080 m3) gives a total mass for the observable universe of 3.35×1054 kg. The WMAP 7-year results estimate that 4.56% of the universe's mass is made up of normal atoms,[17] so this would give an estimate (A) of 1.43×1053 kg, or (B) 1.53×1053 kg, for all the atoms in the observable universe. The fraction of these atoms that make up stars is probably less than 10%.[55]

### Estimation based on the measured stellar density

One way to calculate the mass of the visible matter that makes up the observable universe is to assume a mean stellar mass and to multiply that by an estimate of the number of stars in the observable universe, as seen in the paper 'On the Expansion of the Universe' from the Mathematical Thinking in Physics section of a former NASA educational site, the Glenn Learning Technologies Project. The paper derives its estimate of the number of stars in the Universe from its value for the volume of the "observable universe"

$\frac{4}{3} \pi {S_\mathrm{horizon}}^3 = 9 \times 10^{30}\ \mathrm{ly}^3$

Note however that this volume is not derived from the 46 billion light year radius given by most authors, but rather from the Hubble volume, which is the volume of a sphere with radius equal to the Hubble length (the distance at which galaxies would currently be receding from us at the speed of light), which the paper gives as 13 billion light years. In any case, the paper combines this volume with an estimate of the average stellar density calculated from observations by the Hubble Space Telescope

$\frac{5 \times 10^{21}\ \textrm{stars}}{4 \times 10^{30} \ \textrm{ly}^3} = 10^{-9} \ \textrm{stars}/\textrm{ly}^3 = 1\ \textrm{star} \ \textrm{per}\ \textrm{billion}\ \textrm{ly}^3$, (or 1 star per cube, 1,000 ly to a side (x,y,z))

yielding an estimate of the number of stars in the observable universe of 9 × 1021 stars (9 sextillion (short scale) stars).

Taking the mass of Sol (2 × 1030 kg) as the mean stellar mass (on the basis that the large population of dwarf stars balances out the population of stars whose mass is greater than Sol) and rounding the estimate of the number of stars up to 1022 yields a total mass for all the stars in the observable universe of 3 × 1052 kg.[56] However, aside from the issue that the calculation is based on the Hubble volume, as noted above the WMAP results in combination with the Lambda-CDM model predict that less than 5% of the total mass of the observable universe is made up of baryonic matter (atoms), the rest being made up of dark matter and dark energy, and it is also estimated that less than 10% of baryonic matter consists of stars.

### Estimation based on steady-state universe

Sir Fred Hoyle calculated the mass of an observable steady-state universe using the formula:[57]

$\frac{4}{3}\cdot \pi \cdot \rho \cdot \left(\frac{c}{H}\right)^3$

which can also be stated as

$\frac{c^3}{2GH} \$

or approximately 8 × 1052 kg.

Here H = Hubble constant, ρ = Hoyle's value for the density, G = gravitational constant and c = speed of light.

## Most distant objects

The most distant astronomical object yet announced as of January 2011 is a galaxy candidate classified UDFj-39546284. In 2009, a gamma ray burst, GRB 090423, was found to have a redshift of 8.2, which indicates that the collapsing star that caused it exploded when the universe was only 630 million years old.[58] The burst happened approximately 13 billion years ago,[59] so a distance of about 13 billion light years was widely quoted in the media (or sometimes a more precise figure of 13.035 billion light years),[58] though this would be the "light travel distance" (see Distance measures (cosmology)) rather than the "proper distance" used in both Hubble's law and in defining the size of the observable universe (cosmologist Ned Wright argues against the common use of light travel distance in astronomical press releases on this page, and at the bottom of the page offers online calculators that can be used to calculate the current proper distance to a distant object in a flat universe based on either the redshift z or the light travel time). The proper distance for a redshift of 8.2 would be about 9.2 Gpc,[60] or about 30 billion light years. Another record-holder for most distant object is a galaxy observed through and located beyond Abell 2218, also with a light travel distance of approximately 13 billion light years from Earth, with observations from the Hubble telescope indicating a redshift between 6.6 and 7.1, and observations from Keck telescopes indicating a redshift towards the upper end of this range, around 7.[61] The galaxy's light now observable on Earth would have begun to emanate from its source about 750 million years after the Big Bang.[62]

## Particle horizon

The particle horizon (also called the cosmological horizon, the light horizon, or the cosmic light horizon) is the maximum distance from which particles could have traveled to the observer in the age of the universe. It represents the boundary between the observable and the unobservable regions of the universe,[63] so its distance at the present epoch defines the size of the observable universe.[64] The existence, properties, and significance of a cosmological horizon depend on the particular cosmological model being discussed.

In terms of comoving distance, the particle horizon is equal to the conformal time $\eta_0$ that has passed since the Big Bang, times the speed of light $c$. The quantity $\eta_0$ is given by,

$\eta_0 = \int_{0}^{t_0} \frac{dt'}{a(t')}$

where $a(t)$ is the scale factor of the Friedmann–Lemaître–Robertson–Walker metric, and we have taken the Big Bang to be at $t=0$. In other words, the particle horizon recedes constantly as time passes, and the observed fraction of the universe always increases.[63][65] Since proper distance at a given time is just comoving distance times the scale factor[3] (with comoving distance normally defined to be equal to proper distance at the present time, so $a(t) = 1$ at present), the proper distance to the particle horizon at time $t_0$ is given by[66]

$d_p(t_0) = a(t_0) \int_{0}^{t_0} \frac{dt'}{a(t')}$

The particle horizon differs from the cosmic event horizon, in that the particle horizon represents the largest comoving distance from which light could have reached the observer by a specific time, while the event horizon is the largest comoving distance from which light emitted now can ever reach the observer in the future.[67] At present, this cosmic event horizon is thought to be at a comoving distance of about 46 billion light years.[6] In general, the proper distance to the event horizon at time $t_0$ is given by[66]

$d_e(t_0) = a(t_0) \int_{t_0}^{t_{max}} \frac{dt'}{a(t')}$

where $t_{max}$ is the time-coordinate of the end of the universe, which would be infinite in the case of a universe that expands forever.

A diagram of our location in the observable universe. (Click here for an alternate image.)

## References

1. ^ a b c d Gott III, J. Richard; Mario Jurić, David Schlegel, Fiona Hoyle, Michael Vogeley, Max Tegmark, Neta Bahcall, Jon Brinkmann (2005). "A Map of the Universe". The Astrophysics Journal 624 (2): 463. arXiv:astro-ph/0310571. Bibcode:2005ApJ...624..463G. doi:10.1086/428890.
2. ^ Planck collaboration (2013). "Planck 2013 results. XVI. Cosmological parameters". Submitted to Astronomy & Astrophysics. arXiv:1303.5076.
3. ^ a b Davis, Tamara M.; Charles H. Lineweaver (2004). "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the universe". Publications of the Astronomical Society of Australia 21 (1): 97. arXiv:astro-ph/0310808. Bibcode:2004PASA...21...97D. doi:10.1071/AS03040.
4. ^ Itzhak Bars; John Terning (November 2009). Extra Dimensions in Space and Time. Springer. pp. 27–. ISBN 978-0-387-77637-8. Retrieved 1 May 2011.
5. ^ Frequently Asked Questions in Cosmology. Astro.ucla.edu. Retrieved on 2011-05-01.
6. Lineweaver, Charles; Tamara M. Davis (2005). "Misconceptions about the Big Bang". Scientific American. Retrieved 2008-11-06.
7. ^ Is the universe expanding faster than the speed of light? (see the last two paragraphs)
8. ^ Krauss, Lawrence M.; Robert J. Scherrer (2007). "The Return of a Static Universe and the End of Cosmology". General Relativity and Gravitation 39 (10): 1545–1550. arXiv:0704.0221. Bibcode:2007GReGr..39.1545K. doi:10.1007/s10714-007-0472-9.
9. ^ Using Tiny Particles To Answer Giant Questions. Science Friday, 3 Apr 2009. According to the transcript, Brian Greene makes the comment "And actually, in the far future, everything we now see, except for our local galaxy and a region of galaxies will have disappeared. The entire universe will disappear before our very eyes, and it's one of my arguments for actually funding cosmology. We've got to do it while we have a chance."
10. ^
11. ^ Loeb, Abraham (2002). "The Long-Term Future of Extragalactic Astronomy". Physical Review D 65 (4). arXiv:astro-ph/0107568. Bibcode:2002PhRvD..65d7301L. doi:10.1103/PhysRevD.65.047301.
12. ^ Alan H. Guth (17 March 1998). The inflationary universe: the quest for a new theory of cosmic origins. Basic Books. pp. 186–. ISBN 978-0-201-32840-0. Retrieved 1 May 2011.
13. ^ Constraints on the Topology of the Universe
14. ^ Mota; Reboucas; Tavakol (2010). "Observable circles-in-the-sky in flat universes". arXiv:1007.3466 [astro-ph.CO].
15. ^ "WolframAlpha". Retrieved 29 November 2011.
16. ^ "WolframAlpha". Retrieved 29 November 2011.
17. "Seven-Year Wilson Microwave Anisotropy Probe (WMAP) Observations: Sky Maps, Systematic Errors, and Basic Results" (PDF). nasa.gov. Retrieved 2010-12-02. (see p. 39 for a table of best estimates for various cosmological parameters)
18. ^ Abbott, Brian (May 30, 2007). "Microwave (WMAP) All-Sky Survey". Hayden Planetarium. Retrieved 2008-01-13.
19. ^ Paul Davies (28 August 1992). The new physics. Cambridge University Press. pp. 187–. ISBN 978-0-521-43831-5. Retrieved 1 May 2011.
20. ^ V. F. Mukhanov (2005). Physical foundations of cosmology. Cambridge University Press. pp. 58–. ISBN 978-0-521-56398-7. Retrieved 1 May 2011.
21. ^
22. ^ Universe Might be Bigger and Older than Expected. Space.com (2006-08-07). Retrieved on 2011-05-01.
23. ^ Big bang pushed back two billion years – space – 04 August 2006 – New Scientist. Space.newscientist.com. Retrieved on 2011-05-01.
24. ^ 2 billion years added to age of universe. Worldnetdaily.com. Retrieved on 2011-05-01.
25. ^ Edward L. Wright, "An Older but Larger Universe?"
26. ^ a b c Cornish; Spergel; Starkman; Eiichiro Komatsu (2003). "Constraining the Topology of the Universe". Phys.Rev.Lett. 92 (2004)02 92 (20). arXiv:astro-ph/0310233. Bibcode:2004PhRvL..92t1302C. doi:10.1103/PhysRevLett.92.201302.
27. ^ Levin, Janna. "In space, do all roads lead to home?". plus.maths.org. Retrieved 2012-08-15.
28. ^ http://cosmos.phy.tufts.edu/~zirbel/ast21/sciam/IsSpaceFinite.pdf
29. ^ Bob Gardner's "Topology, Cosmology and Shape of Space" Talk, Section 7. Etsu.edu. Retrieved on 2011-05-01.
30. ^ Vaudrevange; Starkmanl; Cornish; Spergel. Constraints on the Topology of the Universe: Extension to General Geometries. arXiv:1206.2939. Bibcode:2012arXiv1206.2939V.
31. ^ a b SPACE.com – Universe Measured: We're 156 Billion Light-years Wide!
32. ^ Roy, Robert. (2004-05-24) New study super-sizes the universe – Technology & science – Space – Space.com – msnbc.com. MSNBC. Retrieved on 2011-05-01.
33. ^ "Astronomers size up the Universe". BBC News. 2004-05-28. Retrieved 2010-05-20.
34. ^ "MSU researcher recognized for discoveries about universe". 2004-12-21. Retrieved 2011-02-08.
35. ^ Space.com – Universe Might be Bigger and Older than Expected
36. ^ M. J. Geller & J. P. Huchra, Science 246, 897 (1989).
37. ^ Biggest void in space is 1 billion light years across – space – 24 August 2007 – New Scientist. Space.newscientist.com. Retrieved on 2011-05-01.
38. ^ Wall, Mike (2013-01-11). "Largest structure in universe discovered". Fox News.
39. ^ LiveScience.com, "The Universe Isn't a Fractal, Study Finds", Natalie Wolchover,22 August 2012
40. ^ Robert P Kirshner (2002). The Extravagant Universe: Exploding Stars, Dark Energy and the Accelerating Cosmos. Princeton University Press. p. 71. ISBN 0-691-05862-8.
41. ^ "Large Scale Structure in the Local Universe: The 2MASS Galaxy Catalog", Jarrett, T.H. 2004, PASA, 21, 396
42. ^ Massive Clusters of Galaxies Defy Concepts of the Universe N.Y. Times Tue. November 10, 1987:
43. ^ Map of the Pisces-Cetus Supercluster Complex:
44. ^ "Astronomers count the stars". BBC News. July 22, 2003. Retrieved 2006-07-18.
45. ^ "trillions-of-earths-could-be-orbiting-300-sextillion-stars"
46. ^ van Dokkum, Pieter G.; Charlie Conroy (2010). "A substantial population of low-mass stars in luminous elliptical galaxies". Nature 468 (7326): 940–942. arXiv:1009.5992. Bibcode:2010Natur.468..940V. doi:10.1038/nature09578. PMID 21124316.
47. ^ "How many stars?"
48. ^ How many galaxies in the Universe? says "the Hubble telescope is capable of detecting about 80 billion galaxies. In fact, there must be many more than this, even within the observable universe, since the most common kind of galaxies in our own neighborhood are faint dwarfs, which are difficult enough to see nearby, much less at large cosmological distances."
49. ^ WMAP- Content of the Universe. Map.gsfc.nasa.gov (2010-04-16). Retrieved on 2011-05-01.
50. ^ archived version of page from 2005-04-30.
51. ^ Bernard F. Schutz (2003). Gravity from the ground up. Cambridge University Press. pp. 361–. ISBN 978-0-521-45506-0. Retrieved 1 May 2011.
52. ^ Matthew Champion, "Re: How many atoms make up the universe?", 1998
53. ^ 'Is Energy Conserved in General Relativity?' by Michael Weiss and John C. Baez
54. ^ National Solar Observatory. "The Universe".
55. ^ Houjun Mo; Frank van den Bosch; Simon White (28 June 2010). Galaxy Formation and Evolution. Cambridge University Press. ISBN 978-0-521-85793-2. Retrieved 1 May 2011.
56. ^ On the expansion of the Universe (PDF). NASA Glenn Research Centre.
57. ^ Helge Kragh (1999-02-22). Cosmology and Controversy: The Historical Development of Two Theories of the Universe. Princeton University Press. p. 212, Chapter 5. ISBN 0-691-00546-X.
58. ^ a b New Gamma-Ray Burst Smashes Cosmic Distance Record – NASA Science. Science.nasa.gov. Retrieved on 2011-05-01.
59. ^ More Observations of GRB 090423, the Most Distant Known Object in the Universe. Universetoday.com (2009-10-28). Retrieved on 2011-05-01.
60. ^ Attila Meszaros; Balázs; Bagoly; Veres (2009). "Impact on cosmology of the celestial anisotropy of the short gamma-ray bursts". Baltic Astronomy 18: 293–296. arXiv:1005.1558. Bibcode:2009BaltA..18..293M. More than one of |author2= and |last2= specified (help); More than one of |author3= and |last3= specified (help); More than one of |author4= and |last4= specified (help)
61. ^ Hubble and Keck team up to find farthest known galaxy in the Universe|Press Releases|ESA/Hubble. Spacetelescope.org (2004-02-15). Retrieved on 2011-05-01.
62. ^ MSNBC: "Galaxy ranks as most distant object in cosmos"
63. ^ a b Edward Robert Harrison (2000). Cosmology: the science of the universe. Cambridge University Press. pp. 447–. ISBN 978-0-521-66148-5. Retrieved 1 May 2011.
64. ^ Andrew R. Liddle; David Hilary Lyth (13 April 2000). Cosmological inflation and large-scale structure. Cambridge University Press. pp. 24–. ISBN 978-0-521-57598-0. Retrieved 1 May 2011.
65. ^ Michael Paul Hobson; George Efstathiou; Anthony N. Lasenby (2006). General relativity: an introduction for physicists. Cambridge University Press. pp. 419–. ISBN 978-0-521-82951-9. Retrieved 1 May 2011.
66. ^ a b Massimo Giovannini (2008). A primer on the physics of the cosmic microwave background. World Scientific. pp. 70–. ISBN 978-981-279-142-9. Retrieved 1 May 2011.
67. ^ Lars Bergström and Ariel Goobar: "Cosmology and Particle Physics", WILEY (1999), page 65. ISBN 0-471-97041-7