Comparison of two approximation schemes for solving perturbations in a LTB cosmological model

TL;DR

This paper compares two approximation methods for analyzing perturbations in LTB cosmological models, revealing that a commonly used assumption is generally invalid at the relevant order, highlighting the importance of method choice.

Contribution

The study evaluates the compatibility of two perturbation schemes in LTB models, demonstrating the limitations of the Clarkson-Clifton-February assumption at second order.

Findings

The two approaches are generally incompatible.

The Clarkson-Clifton-February assumption is invalid at the order of interest.

Differences between linear and second-order perturbation analyses are clarified.

Abstract

Recently, the present authors studied perturbations in the Lemaitre-Tolman-Bondi cosmological model by applying the second-order perturbation theory in the dust Friedmann-Lemaitre-Robertson-Walker universe model. Before this work, the same subject was studied in some papers by analyzing linear perturbations in the Lemaitre-Tolman-Bondi cosmological model under the assumption proposed by Clarkson, Clifton and February, in which two of perturbation variables are negligible. However, it is a non-trivial issue in what situation the Clarkson-Clifton-February assumption is valid. In this paper, we investigate differences between these two approaches. It is shown that, in general, these two approaches are not compatible with each other. That is, in our perturbative procedure, the Clarkson-Clifton-February assumption is not valid at the order of our interest.