1. The thermal cosmic microwave background radiation

We are in a sea of radiation with spectrum very close to Planck at T = 2.73 K, and isotropic to one part in 10⁵ (after correction for a dipole term that usually is interpreted as the result of our motion relative to the rest frame defined by the radiation). ⁽⁶⁸⁾ The thermal spectrum indicates thermal relaxation, for which the optical depth has to be large on the scale of the Hubble length H₀^-1. We know space now is close to transparent at the wavelengths of this radiation, because radio galaxies are observed at high redshift. Thus the universe has to have expanded from a state quite different from now, when it was hotter, denser, and optically thick. This is strong evidence our universe is evolving.

This interpretation depends on, and checks, conventional local physics with a single metric description of spacetime. Under these assumptions the expansion of the universe preserves the thermal spectrum and cools the temperature as ⁽⁶⁹⁾

(60)

Bahcall and Wolf (1968) point out that one can test this temperature-redshift relation by measurements of the excitation temperatures of fine-structure absorption line systems in gas clouds along quasar lines of sight. The corrections for excitations by collisions and the local radiation field are subtle, however, and perhaps not yet fully sorted out (as discussed by Molaro et al., 2002, and references therein).

The 3 K thermal cosmic background radiation is a centerpiece of modern cosmology, but its existence does not test general relativity.

⁶⁸ The history of the discovery and measurement of this radiation, and its relation to the light element abundances in test (2), is presented in Peebles (1971, pp. 121-9 and 240-1), Wilkinson and Peebles (1990), and Alpher and Herman (2001). The precision spectrum measurements are summarized in Halpern, Gush, and Wishnow (1991) and Fixsen et al. (1996). Back.

⁶⁹ To see this, recall the normal modes argument used to get Eq. (7). The occupation number in a normal mode with wavelength at temperature T is the Planck form = [e^c/kT - 1]^-1. Adiabaticity says is constant. Since the mode wavelength varies as a(t), where a is the expansion factor in Eq. (4), and is close to constant, the mode temperature varies as T 1 / a(t). Since the same temperature scaling applies to each mode, an initially thermal sea of radiation remains thermal in the absence of interactions. We do not know the provenance of this argument; it was familiar in Dicke's group when the 3 K cosmic microwave background radiation was discovered. Back.