2.3 The Expansion of the Universe

In the relativistic Friedmann-Lemaître cosmological model the wavelength of a freely propagating photon is stretched in proportion to the expansion factor from the epoch of emission to detection:

(11)

The first expression defines the redshift z in terms of the ratio of observed wavelength to wavelength at emission. The cosmological expansion parameter a (t) is proportional to the mean distance between conserved particles.

The most direct evidence that the redshift is a result of expansion is the thermal spectrum of the CBR [26]. In a tired light model in a static universe the photons suffer a redshift that is proportional to the distance travelled, but in the absence of absorption or emission the photon number density remains constant. In this case a significant redshift makes an initially thermal spectrum distinctly not thermal and inconsistent with the measured CBR spectrum. One could avoid this by assuming the mean free path for absorption and emission of CBR photons is much shorter than the Hubble length, so relaxation to thermal equilibrium is much faster than the rate of distortion of the spectrum by the redshift. But this opaque universe is quite inconsistent with the observation of radio galaxies at redshifts z ~ 3 at CBR wavelengths. That is, the universe cannot have an optical depth large enough to preserve a thermal CBR spectrum in a tired light model. In the standard world model the expansion has two effects: it redshifts the photons, as a (t), and it dilutes the photon number density, as n a (t)^-3. The result is to cool the CBR while keeping its spectrum thermal. Thus the expanding universe allows a self-consistent picture: the CBR was thermalized in the past, at a time when when the universe was denser, hotter, and optically thick.

I have not encountered any serious objection to this argument; the issue is the expansion factor. In the relativistic Friedmann-Lemaître model the expansion of the universe traces back at least as far as redshift z ~ 10¹⁰, when the light elements formed in observationally reasonable amounts [18]. In the model of Arp et al. [27] the expansion and cooling traces back to a redshift only moderately greater than the largest observed values, z ~ 5, when there would have been a burst of creation of matter and radiation followed by rapid clearing of the dust that thermalized the radiation. The Arp et al. picture for the origin of the light elements has not been widely debated. If it were agreed that it is viable then a choice between this and the Friedmann-Lemaître model would depend on other tests, such as the angular fluctuations in the CBR, as discussed next.