Size of the Universe

The size of the universe is based on the the comoving distance from Earth to the edge of the, which is about 14.26 gigaparsecs (46.5 billion light years or 4.40×1026 meters) in any direction. The observable universe is thus a sphere with a diameter of about 28.5 gigaparsecs (93 Gly or 8.8×1026 m). Assuming that space is roughly flat, this size corresponds to a comoving volume of about $1.22 Gpc^{3}$ ($4.22 Gly^{3}$ or $3.57 m3$).

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 13.8 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. > 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

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

WMAP nine-year results combined with other measurements give the redshift of photon decoupling as z = $1,091.64$, which implies that the scale factor at the time of photon decoupling would be $1/undefined$. 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.