More examples of structure formation in the Lemaître-Tolman model

Abstract

In continuing our earlier research, we find the formulas needed to determine the arbitrary functions in the Lema\^{\i}tre-Tolman (LT) model when the evolution proceeds from a given initial velocity distribution to a final state that is determined either by a density distribution or by a velocity distribution. In each case the initial and final distributions uniquely determine the LT model that evolves between them, and the sign of the energy function is determined by a simple inequality. We also show how the final density profile can be more accurately fitted to observational data than was done in our previous paper. We work out new numerical examples of the evolution: the creation of a galaxy cluster out of different velocity distributions, reflecting the current data on temperature anisotropies of cosmic microwave background, the creation of the same out of different density distributions, and the creation of a void. The void in its present state is surrounded by a nonsingular wall of high density.