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[14] (93 Gly or 8.8¡¿1026 m).[15] 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, which occurred around 13.7 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.[citation needed] 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.
WMAP seven-year results give the redshift of photon decoupling as z=1090.89 which implies that the scale factor at the time of photon decoupling would be 1⁄1091.89. 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.
13.7 billion light-years The age of the universe is estimated to be 13.7 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 13.7 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.
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 .
27.4 billion light-years This is a diameter obtained from the (incorrect) radius of 13.7 billion light-years.
78 billion light-years In 2003, Cornish et al. 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.
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. 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."
180 billion light-years This estimate accompanied the age estimate of 15.8 billion years in some sources; it was obtained by adding 15% to the figure of 156 billion light years.