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1.1. Redshift

Light emitted from a comoving galaxy located at Thetag at time te will reach an observer situated at Thetao ident 0 at a later time to, where

Equation 5 (5)

Equation 5 provides the relation among Thetag, to, and te. For a comoving galaxy, Thetag is unchanged so that differentiating eq. 5 leads to

Equation 6 (6)

This result relates the evolution of the universe (ao / ae) as the photon travels from emission to observation, to the change in its frequency (nu) or wavelength (lambda). As the universe expands (or contracts!), wavelengths expand (contract) and frequencies decrease (increase). The redshift of a spectral line is defined by relating the wavelength at emission (the "lab" or "rest-frame" wavelength lambdae) to the wavelength observed at a later time to, lambdao.

Equation 7 (7)

Since the energies of photons are directly proportional to their frequencies, as the universe expands photon energies redshift to smaller values: Egamma = h nu ==> Egamma propto (1 + z)-1. For all particles, massless or not, de Broglie told us that wavelength and momentum are inversely related, so that: p propto lamabda-1 ==> p propto (1 + z)-1. All momenta redshift; for non-relativistic particles (e.g. galaxies) this implies that their "peculiar" velocities redshift: v = p/M propto (1 + z)-1.

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