More examples of structure formation in the Lemaitre-Tolman model

TL;DR

This paper derives formulas for the Lemaitre-Tolman model to determine arbitrary functions based on initial and final distributions, improving data fitting and illustrating structure formation through numerical examples.

Contribution

It provides new formulae for the L-T model linking initial velocities to final density or velocity states, with enhanced data fitting and detailed numerical examples.

Findings

Successful modeling of galaxy cluster formation from velocity distributions

Improved accuracy in fitting final density profiles to observational data

Illustration of void creation with surrounding high-density wall

Abstract

In continuing our earlier research, we find the formulae needed to determine the arbitrary functions in the Lemaitre-Tolman 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 L-T 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 CMB, 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.