Alternative Methods of Describing Structure Formation in the Lemaitre-Tolman Model

TL;DR

This paper introduces new methods for specifying and constructing Lemaitre-Tolman models by defining various boundary and asymptotic conditions, expanding the ways to design models with specific properties.

Contribution

It presents novel approaches for deriving LT model functions from data, including conditions like simultaneous big bang and homogeneous density, enhancing model customization.

Findings

Multiple new boundary conditions for LT models

Methods to obtain LT functions from specified data

Expanded possibilities for model design

Abstract

We describe several new ways of specifying the behaviour of Lemaitre-Tolman (LT) models, in each case presenting the method for obtaining the LT arbitrary functions from the given data, and the conditions for existence of such solutions. In addition to our previously considered `boundary conditions', the new ones include: a simultaneous big bang, a homogeneous density or velocity distribution in the asymptotic future, a simultaneous big crunch, a simultaneous time of maximal expansion, a chosen density or velocity distribution in the asymptotic future, only growing or only decaying fluctuations. Since these conditions are combined in pairs to specify a particular model, this considerably increases the possible ways of designing LT models with desired properties.