Observable Universe - Size

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 (93 Gly or 8.8×1026 m). 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. 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.