Observable universe

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In Big Bang cosmology, the observable universe is the region of space bounded by a sphere, centered on the observer, that is small enough that we might observe objects in it, i.e. there has been sufficient time for light emitted by an object to arrive at the observer. Every position has its own observable universe which may or may not overlap with the one centered around the Earth.

The word observable used in this sense has nothing to do with whether modern technology actually permits us to detect radiation from an object in this region. It simply means that it is possible for light or other radiation from the object to reach an observer on earth. In practice, we can only observe objects as far as the surface of last scattering, before which the universe was opaque to photons. However, it may be possible to infer information from before this time through the detection of gravitational waves.

The universe versus the observable universe

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, such as cosmic inflation require a universe much larger than the observable universe. No evidence exists to suggest that the boundary of the observable universe corresponds precisely to the physical boundary of the universe (if such a boundary exists); this is exceedingly unlikely in that it would imply that the Earth is exactly at the center of the universe, in violation of the cosmological principle. It is likely that the galaxies within our visible universe represent only a minuscule fraction of the galaxies in the universe.

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. A 2004 paper claims to establish a lower bound of 24 gigaparsecs (78 billion light-years) on the diameter of the universe, based on matching-circle analysis of the WMAP data.

Size

The comoving distance from the Earth to the edge of the visible universe (also called cosmic light horizon) is about 14 billion parsecs (46.5 billion light-years) in any direction. This defines the comoving radius of the observable universe. The observable universe is thus a sphere with a diameter of 28-29 billion parsecs (92–94 billion light-years). Since space is roughly flat, this size corresponds to a comoving volume of about

$frac\{4\}\{3\}\; times\; pi\; times\; mathrm\{R\}^3\; =\; 4.20\; times\; 10^\{32\}text\{\; ly\}^3$

or 3.56×10⁸⁰ cubic meters.

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 about 13.7 billion years ago by matter that has, in the intervening time, condensed into galaxies. Those galaxies are now about 46 billion light-years from us, but at the time the light was emitted, that matter was only about 40 million light-years away from the matter that would eventually become the Earth. See comoving coordinates.

Misconceptions

Many secondary sources have reported a wide variety of incorrect figures for the size of the visible universe. Some of these are listed below.

• 13.7 billion light-years. The age of the universe is about 13.7 billion years. While it is commonly understood that nothing travels faster than light, it is a common misconception that the radius of the observable universe must therefore amount to only 13.7 billion light-years. This reasoning only makes sense if the universe is the flat spacetime of special relativity; in the real universe, spacetime is highly curved on cosmological scales, which means that 3-space (which is roughly flat) is expanding, as evidenced by Hubble's law. Distances obtained as the speed of light times a cosmological time interval have no direct physical significance.
• 15.8 billion light-years. This is obtained in the same way as the 13.7 billion light year figure, but starting from an incorrect age of the universe which was reported in the popular press in mid-2006 . For an analysis of this claim and the paper that prompted it, see .
• 27 billion light-years. This is a diameter obtained from the (incorrect) radius of 13.7 billion light-years.
• 78 billion light-years. This is a lower bound (not an estimate) for the size of the whole universe (not the observable universe). If the universe is smaller than the observable universe, then light has had time to circumnavigate it since the big bang, producing multiple images of distant objects in the sky. Cornish et al looked for such an effect at scales of up to 24 gigaparsecs (78 billion light years) and failed to find it. 24 gigaparsecs is simply the upper limit of the search space of this study; it has no physical significance.
• 156 billion light-years. This figure was obtained by doubling 78 billion light-years on the assumption that it is a radius. Since 78 billion light-years is already a diameter (or rather a circumference), the doubled figure is meaningless even in its original context. This figure was very widely reported .
• 180 billion light-years. This estimate accompanied the age estimate of 15.8 billion years in some sources; it was obtained by incorrectly adding 15 percent to the incorrect figure of 156 billion light years.

Matter content

The observable universe contains about 3 to 7 × 10²² stars, organized in more than 80 billion galaxies, which themselves form clusters and superclusters.

Two back-of-an-envelope calculations give the number of atoms in the observable universe to be around 10⁸⁰.

1. The critical density of the universe is $3\; H^2/8\; pi\; G$, which works out to be 1×10⁻²⁶ kg/m³ or about 5 atoms of hydrogen/m³. It is believed that only 4 percent of the critical density is in the form of normal atoms, so this leaves 0.2 hydrogen atoms/m³. Multiplying this by the volume of the visible universe, you get about 7×10⁷⁹ hydrogen atoms.
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 ignores many possible atom sources.

Mass of the observable universe

The mass of the observable universe can be estimated based on either density or size.

Estimation based on the measured mass density

Estimates of its density are obtained by studying fluctuations in cosmic microwave background radiation, superclusters, and Big Bang nucleosynthesis. These yield a density estimate of $3\; times\; 10^\{-27\}\; textrm\{kg\}/\{textrm\{m\}^3\}$. Estimates of the size of the observable universe vary, but a size estimate of $1.4\; times\; 10^\{10\}$ light years yields a mass estimate of $3\; times\; 10^\{52\}\; textrm\{kg\}$.

Estimation based on the measured stellar density

Another way to calculate the mass of the observable universe is to assume a mean solar mass and to multiply that by an estimate of the number of stars in the observable universe. The estimate of the number of stars in the universe is in turn derived from the volume of the observable universe ($frac\{4\}\{3\}\; pi\; \{S\_textrm\{horizon\}\}^3\; =\; 9\; times\; 10^\{30\}\; textrm\{ly\}^3$) and a stellar density calculated from observations by the Hubble Space Telescope ($frac\{5\; times\; 10^\{21\}\; textrm\{stars\}\}\{4\; times\; 10^\{30\}\; textrm\{ly\}^3\}\; =\; 10^\{-9\}\; textrm\{stars\}/textrm\{ly\}^3$) yielding an estimate of the number of stars in the observable universe of $9\; times\; 10^\{21\}\; textrm\{stars\}$. Assuming the mass of Sol ($2\; times\; 10^\{30\}\; textrm\{kg\}$) as the mean solar 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 $10^\{22\}\; textrm\{stars\}$ yields a mass of the observable universe as $3\; times\; 10^\{52\}\; textrm\{kg\}$.

Hoyle calculates the mass of an observable steady-state universe using the formula $frac\{4\}\{3\}cdot\; pi\; cdot\; rho\; cdot\; (frac\{c\}\{H\})^3$, or $frac\{c^3\}\{2GH\}$.

See also

External links

• Cosmology FAQ
• Hubble, VLT and Spitzer Capture Galaxy Formation in the Early Universe
• Star Survey reaches 70 sextillion
• Inflation and the Cosmic Microwave Background, Lineweaver 2003
• Animation of the cosmic light horizon
• Logarithmic Maps of the Universe

References

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Last updated on Wednesday March 05, 2008 at 14:43:57 PST (GMT -0800)
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