Primeval black holes and galaxy formation.

A scheme of galaxy formation is presented, in which the hypothesis of primeval fluctuations over galactic scales is replaced by the hypothesis that a certain fraction of the mass of the early universe is in the form of black holes of about one solar mass each. This hypothesis is shown to lead to a simple relationship among the parameters of amplitude, slope, and present density, wherein the amplitude can be theoretically determined from the value of the slope and the only free parameter would be the present density, which would have an invisible component in the form of black holes. Equations are derived for instability over scales larger and smaller than the horizon and for the thermal history of the gas after recombination. It is proposed that with this model, galaxy and cluster formation can be realized at the correct redshifts, and massive halos of galaxies and the hidden mass in clusters required by virial theorem arguments can be attributed to black holes.