Fluctuations at the Threshold of Classical Cosmology

The "threshold epoch" of classical cosmology is first discussed from a classical point of view. It is shown that if the density fluctuations at this epoch are proportional to $N^{-n}$ (where $N$ is the number of particles in a disturbance), then $n$ must exactly, or very closely, equal the value $\frac{2}{3}$ in order that such fluctuations develop into protogalaxies. This result is independent of the value of the threshold epoch, and of the equation of state for the very early universe. Arguments of a speculative nature are then presented which indicate that the threshold epoch occurs at the Planck density. It is also proposed that the initial conditions of galaxy formation are metric fluctuations at the threshold epoch of classical cosmology. The evidence in favor of this theory is (i) the density fluctuation obeys the $n=\frac{2}{3}$ rule, and (ii) the spin fluctuation gives an eventual angular momentum of the order $N^{\frac{4}{3}}\hslash$, in reasonable agrement with that of the Galaxy.