Hubble's Law and Scale Factors

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Hubble’s Law (1929)

Hubble’s Law is an empirical law stating that, on large scales, recessional velocity is proportional to distance from observer.

where , the Hubble parameter, is not constant, but can vary slowly with time. By convention, is often expressed as , where 1 parsec (pc) , is the distance at which 1 AU appears as 1 arcsec on the sky. The Hubble Space Telescope Key Project (Freedman et al. ApJ 553, 47, 2001) measured the present day value of Hubble Constant , giving us that the current timescale for the expansion of the universe is .

The Scale Factor,

relates physical () and comoving () coordinates in an expanding universe:

Thus, the two components of physical velocity are (the Hubble expansion parameter) and (the peculiar velocity, or motion relative to expansion) By convention, today and .