cosmological redshift

Cosmological redshift is redshift (lengthening of wavelengths due to Doppler effects) of distant objects due to the Hubble expansion (the further-distant an object, the greater is the receding radial velocity). The redshift parameter (z) is used as a measure of distance and time regarding such objects:

     observed wavelength - rest wavelength
z =  —————————————————————————————————————
              rest wavelength

The relationship between z and the recessional velocity, ignoring relativity (which is OK for low velocities) is z=v/c, where v is recessional velocity and c is the light speed. Incorporating special relativity using the Lorentz transformation (better for higher velocities) is:

1 + z = γ ( 1 + v/c )

where γ is the Lorentz factor, (1-V²/C²)^-½. This is equivalent to:

              1 + v/c
1 + z = sqrt( ——————— )
              1 - v/c

If a body's redshift is determined, assuming the redshift is cosmological, a distance estimate can be calculated using the redshift and the Hubble constant and Hubble's law. Measured redshift, however, is also affected by the peculiar velocity of the object: independent of the Hubble expansion, objects are generally moving relative to each other and an accurate distance-determination includes determination of the object's peculiar velocity (relative to the Hubble flow) to determine how much it affects the measured redshift. For extreme distances, e.g., to the furthest quasars, the cosmological redshift likely dominates and the measured redshift should be a reasonable approximation of the cosmological redshift and often the best practical distance determination.

The adjective-phrase high redshift, e.g., high redshift galaxy, indicates the object's distance and z-value are large. Low redshift means relatively nearby, for example, a z-value considerably less than 1; this hardly needs mention for objects within the Local Group, more likely used to indicate galaxies in nearby galaxy clusters.

Below are some calculated values of z using a Hubble constant of 70 km/s/Mpc, using the above two calculation methods, demonstrating the discrepancies. "Gyears" (for gigayears) is how far in the past we're viewing the body and is also its distance in billions of light-years.

For the largest redshifts, corresponding distances and times are further affected by the universe's density, calculated to be a little smaller than the numbers shown above. See "Distances table" for redshifts/distances to example astronomical objects and times since astronomical events.