**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
~ 10^{11}
*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 ×
10^{6} (
*h*^{2})^{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
*t*_{i}, 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 *t*_{i}. The
important point to note is that if
*t*_{i} 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*_{} < 10^{12} K. For
*T*_{} > 10^{12} K (the hadron and pre-hadron
era), the strong interaction becomes important because mesons are
copiously produced. But when
*T*_{} = 10^{12} 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).