Relativistic Theory of the Behavior of Irregularities in an Expanding World Model

This chapter presents the full relativistic analysis of the evolution of mass clustering. The full relativistic theory is needed to deal with three important aspects of density irregularities in the early universe. First, when the pressure is high the relativistic active gravitational mass and inertial mass associated with pressure affect the dynamics. Second, when the mean density is high, a fluctuation of even modest fractional amount containing a modest mass can have a large effect on the space curvature. One is thus led to deal with the interaction of speculations on the nature of the mass distribution and of the geometry in the early universe. Third, the horizon shrinks to zero at the time of the big bang: the seed fluctuations out of which galaxies might form were larger than the horizon and so were not in causal connection reckoned from the time of the big bang. Of course, this curious point applies as well to the homogeneous background: it was somehow contrived that all parts of the universe now visible were set expanding with quite precise uniformity even though an observer could not have discovered this much before the present epoch.

Behavior of Irregularities in the Distribution of Matter: Newtonian Approximation

This chapter examines the behavior of a given mass distribution in the Newtonian approximation. Discussion of how irregularities in the matter distribution behave in an expanding universe is greatly simplified by the fact that a limiting approximation of general relativity, Newtonian mechanics, applies in a region small compared to the Hubble length. The rest of the universe can affect the region only through a tidal field. Though the point was clearly made by Georges Lemaître, it has not always been recognized that the Newtonian approximation is not a model but a limiting case valid no matter what is happening in the distant parts of the universe. Because of the importance of this result, the chapter discusses it at some length.

Scenarios

This chapter describes some of the attempts to trace the links between theory and observation, showing how the character of the matter distribution we observe developed out of reasonable conditions in the early universe. Opinions on what the universe might have been like at high redshift span the range from primeval chaos to a distribution well ordered in the large but more or less chaotic or turbulent on small scales, to a universe quite precisely homogeneous and isotropic. It is not surprising that the arguments that have been advanced in favor of each scenario all make good points that to some seem compelling. The principle that has been adopted in this book and that argues against all variants of the primeval chaos scenario is that gravity tries to enhance density irregularities, not disperse them: as long as gravity is the dominant force it is hard to see how the universe could do other than grow more irregular. The chapter then considers the nature of protogalaxies and protoclusters.