Expansionsfaktorn

Expansionsfaktorn, or expansion factor, is a dimensionless function a(t) that describes the expansion of space in cosmological models. It is the scale factor in the Friedmann-Lemaître-Robertson-Walker metric and relates the proper distance between comoving points by D(t) = a(t) χ, where χ is the comoving distance. The function is typically normalized so that a(t0) = 1 at the present time t0.

The Hubble parameter is defined as H(t) = ȧ(t) / a(t), describing the rate of expansion. For distant objects, the recession velocity is approximately v ≈ H(t) D(t) for small separations. Redshift z of light from a distant object is related to the scale factor by a(t) = 1/(1+z) when a(t0) = 1, so higher redshift corresponds to a smaller scale factor at the time of emission.

The expansion factor evolves according to the Friedmann equations, which connect ȧ, a, and the energy content of the universe (matter, radiation, dark energy) as well as spatial curvature. The history of a(t) determines distance measures such as luminosity distance and angular diameter distance, which are used to compare cosmological models with observations from supernovae, the cosmic microwave background, and baryon acoustic oscillations.

Significance: the expansion factor encodes the history of cosmic expansion; it is not a physical velocity of galaxies, and bound systems do not participate in the expansion. The concept is central to cosmology and informs the interpretation of observational data and early-universe physics.