On the Validity of a Factorizable Metric Ansatz in String Cosmology

TL;DR

This paper investigates the validity of a factorizable metric ansatz in string cosmology by analyzing a toy model in the RSI framework, confirming the ansatz's consistency through a revised gradient expansion method.

Contribution

It revises the gradient expansion method to test the factorizable metric ansatz and demonstrates its validity within a toy RSI model in string cosmology.

Findings

The effective 4D action matches the one derived from the factorizable metric ansatz.

The revised method confirms the ansatz's validity in the toy model.

Supports the use of the factorizable metric ansatz in string cosmology studies.

Abstract

To support the validity of a factorizable metric ansatz used in string cosmology, we investigate a toy problem in RSI model. For this purpose, we revise the gradient expansion method to conform to the factorizable metric ansatz. By solving the 5-dimensional equations of motion and substituting the results into the action, we obtain the 4-dimensional effective action. It turns out that the resultant action is equivalent to that obtained by assuming the factorizable metric ansatz. Our analysis gives the support of the validity of the factorizable metric ansatz.