Mass of the Observable Universe

For a general discussion of the universe, see Universe.

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, (see Big Bang cosmology). 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, with future technology, it may be possible 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, light from distant galaxies will have had more time to travel, so some regions not currently observable will become observable. 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]

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

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 would only make sense if the flat, static Minkowski spacetime conception under special relativity were correct. 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]
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] For an analysis of this claim and the paper that prompted it, see the following reference at the end of this article.[24]
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.[25] 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,[26][27] 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.[28] 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."[25] 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.[29]
156 billion light-years
This figure was obtained by doubling 78 billion light-years on the assumption that it is a radius.[30] 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),[25] the doubled figure is incorrect. This figure was very widely reported.[30][31][32] 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."[33]
180 billion light-years
This estimate accompanied the age estimate of 15.8 billion years in some sources;[34] 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 galaxy groups, galaxy clusters, superclusters, sheets, walls and filaments, which 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",[35] 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.[36] 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.[37]

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.[38] 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.[39]

Observations

Another indicator of large-scale structure is the 'Lyman-alpha forest'. This is a collection of absorption lines that appear in the spectra 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.[41][42]

Mass of ordinary matter

The mass of the universe is often quoted as 1050 tons or 1053 kg.[43] In this context, mass refers to ordinary matter and includes the interstellar medium (ISM) and the intergalactic medium (IGM). However, it excludes dark matter and dark energy. Three calculations substantiate this quoted value for the mass of ordinary matter in the universe: Estimates based on critical density, extrapolations from number of stars, and estimates based on steady-state. The calculations obviously assume a finite universe.

Estimates based on critical density

Critical Density is the energy density where the expansion of the universe is poised between continued expansion and collapse.[44] 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 density value. At this condition, the calculation for $\rho_c$ critical density, is):[45]

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

where G is the gravitational constant. From The European Space Agency's Planck Telescope results: $H_0$, is 67.15 kilometers per second per mega parsec. This gives a critical density of 0.85×10 kg/m3 (commonly quoted as about 5 hydrogen atoms/m3). This density includes four significant types of energy/mass: ordinary matter (4.8%), neutrinos (0.1%), cold dark matter (26.8%), and dark energy (68.3%).[2] Note that although neutrinos are defined as particles like electrons, they are listed separately because they are difficult to detect and so different from ordinary matter. Thus, the density of ordinary matter is 4.8% times the total critical density calculated or 4.08×10 kg/m3. To convert this density to mass we must multiply by volume, a value based on the radius of the "observable universe". Since the universe has been expanding for 13.7 billion years, the comoving distance (radius) is now about 46.6 billion light years. Thus, volume (4/3 π r3) equals 3.58×1080 m3 and mass of ordinary matter equals density (4.08×10 kg/m3) times volume (3.58×1080 m3) or 1.46×1053 kg.

Extrapolation from number of stars

There is currently no way to know exactly the number of stars, but from current literature, the range of 1022 to 1024 is normally quoted.[46][47][48][49] One way to substantiate this range is to estimate the number of galaxies and multiply by the number of stars in an average galaxy. The 2004 Hubble Ultra-Deep Field image contains an estimated 10,000 galaxies.[50] The patch of sky in this area, is 3.4 arc minutes on each side. For a relative comparison, it would require over 50 of these images to cover the full moon. If this area is typical for the entire sky, there are over 100 billion galaxies in the universe.[51] More recently, in 2012, Hubble scientists produced the Hubble Extreme Deep Field image which showed slightly more galaxies for a comparable area.[52] However, in order to compute the number of stars based on these images, we would need additional assumptions: the percent of both large and dwarf galaxies; and, their average number of stars. Thus, a reasonable option is to assume 100 billion average galaxies and 100 billion stars per average galaxy. This results in 10 22 stars. Next, we need average star mass which can be calculated from the distribution of stars in the Milky Way. Within the Milky Way, if a large number of stars are counted by spectral class, 73% are class M stars which contain only 30% of the Sun's mass. Considering mass and number of stars in each spectral class, the average star is 51.5% of the Sun's mass.[53] The Sun's mass is 2×1030 kg. so a reasonable number for the mass of an average star in the universe is 1030 kg. Thus, the mass of all stars equals the number of stars (1022) times an average mass of star (1030 kg) or 1052 kg. The next calculation adjusts for Interstellar Medium (ISM) and Intergalactic Medium (IGM). ISM is material between stars: gas (mostly hydrogen) and dust. IGM is material between galaxies, mostly hydrogen. Ordinary matter (protons, neutrons and electrons) exists in ISM and IGM as well as in stars. In the reference, "The Cosmic Energy Inventory“, the percentage of each part is defined: stars - 5.9%, Interstellar Medium (ISM) - 1.7%, and Intergalactic Medium (IGM) - 92.4%.[54] Thus, to extrapolate the mass of the universe from the star mass, divide the 1055 kg mass calculated for stars by 5.9%. The result is 1.7×1053 kg for all the ordinary matter.

Sir Fred Hoyle calculated the mass of an observable steady-state universe using the formula:[55]

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

which can also be stated as [56]

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

Here H = Hubble constant, ρ = Hoyle's value for the density, G = gravitational constant and c = speed of light. This calculation yields approximately 0.92×1053 kg; however, this represents all energy/matter and is based on the Hubble volume, which is the volume of a sphere with radius equal to the Hubble length or about 13.7 billion light years. The critical density calculation above was based on the comoving distance 46.6 billion light years radius. Thus, the Hoyle equation mass/energy result must be adjusted for increased volume. The comoving distance (radius) gives a volume about 39 times greater (46.7 cubed divided by 13.7 cubed). However, as volume increases, ordinary matter and dark matter would not increase, only dark energy increases with volume. Thus, assuming ordinary matter and dark matter at 27.9% of the total mass/energy and other 72.1% for dark energy, the amount of total mass/energy for the steady-state calculation would be: mass of ordinary matter and dark matter (27.9% times 0.92×1053 kg) plus the mass of dark energy ((72.1% times 0.92×1053 kg) times increased volume (39)). This equals: 2.61×1054 kg . As noted above in the "Estimating based on critical density", ordinary matter is 4.8% of all energy/matter. If the Hoyle result is multiplied by this percent, the result for ordinary matter is 1.25×1053 kg.

In summary, the three independent calculations produced reasonably close results: 1.46×1053 kg, 1.7×1053 kg, and 1.25×1053 kg. The average is 1.47×1053 kg. The key assumptions using the Extrapolation from Star Mass method were number of stars (1022) and percent of ordinary matter in stars (5.9%). The key assumptions using Critical Density were comoving distance of universe (46.6 billion light years) and percent of ordinary matter in all matter (4.8%). The Hoyle steady-state method assumed the comoving distance and a percent of dark energy (72.1%). Both Critical Density and the Hoyle steady-state equation also used the Hubble constant (67.15 km/s/Mpc).

Matter content - number of atoms

Assuming the mass of ordinary matter is about 1.47×1053 kg (reference previous section) and assuming all atoms are hydrogen atoms (which in reality make up about 74% of all atoms in our galaxy by mass, see Abundance of the chemical elements), calculating the total number of atoms in the universe is straight forward. Divide the mass of ordinary matter by the mass of a hydrogen atom (1.47×1053 kg divided by 1.67×10 kg). The result is approximately 1080 hydrogen atoms.

The most distant

Horizons

Main article: cosmological horizon

The limit of observability in our universe is set by a set of cosmological horizons which limit, based on various physical constraints, the extent to which we can obtain information about various events in the universe. The most famous horizon is the particle horizon which sets a limit on the precise distance that can be seen due to the finite age of the Universe. Additional horizons are associated with the possible future extent of observations (larger than the particle horizon owing to the expansion of space), an "optical horizon" at the surface of last scattering, and associated horizons with the surface of last scattering for neutrinos and gravitational waves.

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