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The Expanding Universe
Cosmological
Redshift
The
discovery of the linear relationship between redshift, interpreted as
recessional velocity, and distance yields a straightforward
mathematical expression for Hubble's Law as follows:Photons
propagating through the expanding space are stretched between their
point of emission emission
(em) and their point of observation (obs), creating an increase in wavelength: the cosmological redshift.
(1+z) is
the factor by which the universe has expanded while the photon was
travelling towards the observer. If t_{obs} is the present
time, then a(t_{obs})=1, and the cosmic scale factor at the
time of emission is
e. g.:
for a cosmological redshift of z=3 the cosmic scale factor at the time of emission was a=1/4. v =
recession velocity, in km/sec
H_{0} = Hubble Parameter (today), H0 = (70 +/ 7) km/sec/Mpc D = (comoving) distance from the galaxy to the observer, in Mpc H_{0} may be interpreted as the rate of expansion of the Universe, and the "Hubble time" 1/H_{0} as the current age of the universe. 
