Rick's Cosmology Tutorial: Chapter 9 Abstract

We have seen in Chapter 8 that the formation of neutral hydrogen atoms from the previously free electrons and protons starts about 185,000 years after the Big Bang. Because free electrons scatter light, the universe is therefore opaque before this time. By 363,000 years just less than 1% of the free electrons are left.

The density of the universe by this time is low, and hence it is to be expected that the universe will become transparent as long as the number of free electrons is sufficiently small. The condition that the universe as a whole is transparent is an onerous one. It requires the mean free path of a photon to be comparable with the size of the universe. In this Chapter we show that the absolute density of free electrons is sufficiently small to cause the universe to become transparent during the active period of recombination (defined as the period within which the free electron density falls from 99% to 1% of its initial value). Specifically, transparency occurs at about 310,000 years. Whilst the onset of transparency is obviously caused by the reduction in the free electron density, it is coincidental that transparency occurs during the active period of recombination.

The time of universal transparency depends upon the absolute electron density, and hence upon the photon:baryon ratio. The coincidence between the times of transparency and recombination is a result of the photon:baryon ratio taking the value it does, namely ~2 x 10^9. Thus, for photon:baryon ratios which are two orders of magnitude larger, the universe is always transparent. For photon:baryon ratios which are one or two orders of magnitude smaller, the universe does become transparent, but not until the free electron fraction drops below 1%.

Thus, postulating that the times of transparency and recombination should be the same, for some reason, would provide a means of 'deducing' the required photon:baryon ratio. However, there is no obvious reason to require the equality of the transparency and recombination times.

Timeline of the universe: What the WMAP satellite can see - the Cosmic Microwave Background as far back as the period of recombination/transparency at about 360,000 years