1.2.2. "Extra" Relativistic Energy

Suppose there is some new physics beyond the standard model of particle physics which leads to "extra" relativistic energy so that _{R R}' _R + _X; hereafter, for convenience of notation, the subscript R will be dropped. It is useful, and conventional, to account for this extra energy in terms of the equivalent number of extra neutrinos: N _X / (Steigman, Schramm, & Gunn 1977 (SSG); see also Hoyle & Tayler 1964, Peebles 1966, Shvartsman 1969). In the presence of this extra energy, prior to e^± annihilation

(1.21)

In this case the early universe would expand faster than in the standard model. The pre-e^± annihilation speedup in the expansion rate is

(1.22)

After e^± annihilation there are similar, but quantitatively different changes

(1.23)

Armed with an understanding of the evolution of the early universe and its particle content, we may now proceed to the main subject of these lectures, primordial nucleosynthesis.