3.2. Origin of fluctuations
The fate of a density perturbation once it has come within the horizon will be considered in detail in Section 4, where we show that no growth is possible until the background radiation temperature becomes low enough to allow the protons and electrons to recombine. This occurs at a redshift 1500, hence there is only a very limited time for fluctuations to grow into bound systems via gravitational instability. Consequently, in order to have made galaxies of mass ~ 1011 M by the present epoch, rather large fluctuations, m / m 10-3 are required at the time a galactic mass entered the horizon. This occurred when the background radiation had the fairly modest temperature of T 1.6 × 106 ( h2)1/3 K, hence it is extremely unlikely that, any physical process operating at these temperatures could have spontaneously generated fluctuations of the required amplitude. One might speculate that at some earlier epoch ti, some as yet unknown process gave rise to pressure inhomogeneities which generated density fluctuations, but as we have seen from Eq. (3.18), pressure inhomogeneities of the same order, i.e. 10-3, are required on galactic scales at time ti. The important point to note is that if ti is chosen small enough to allow reasonable speculation on the microphysics, the total mass within the horizon is small enough that even order unity effects on the horizon scale are unlikely to be of any importance on galactic scales (Hogan, 1980). For example, the physics of the early Universe is fairly well understood for temperatures T < 1012 K. For T > 1012 K (the hadron and pre-hadron era), the strong interaction becomes important because mesons are copiously produced. But when T = 1012 K, the total mass enclosed within the horizon is only 0.6 M, thus since causality limits the scales over which order unity fluctuations could be produced to ct, one could at best produce non-linear lumps of mass 0.6 M. These grains do produce larger scale fluctuations, but with a mass spectrum proportional to M-7/6 (Zel'dovich, 1965; Peebles, 1974b). Unfortunately, this does not suffice to be of interest for galaxy formation unless the grains form at an implausibly late epoch (Carr and Silk, 1983).