Expanding AdS5 Branes: Time Dependent Eigenvalue Problem and Production of Particles

TL;DR

This paper investigates the effects of a time-dependent metric on scalar fields in brane-world scenarios with positive cosmological constant, analyzing eigenvalue problems and particle production during rapid expansion phases.

Contribution

It introduces a detailed analysis of Kaluza-Klein mass eigenvalues in time-dependent brane-world models with positive cosmological constant and examines particle production during rapid brane expansion.

Findings

Eigenvalue problem solutions for time-dependent metrics with small ta.

Approximate particle production during rapid de Sitter expansion.

Insights into scalar field behavior in non-fine-tuned brane scenarios.

Abstract

An analysis is first given of the situation where a scalar field is contained between two fixed, spatially flat, branes. The usual fine-tuning (RS) condition is relaxed, and the branes are allowed to possess a positive effective cosmological constant \lambda. We first analyze the eigenvalue problem for the Kaluza-Klein masses when the metric is time dependent, and consider in detail the case when \lambda is small. Thereafter we consider, in the case of one single brane, the opposite limit in which \lambda is large, acting in a brief period of time T, and present a "sudden approximation" calculation of the energy produced on the brane by the rapidly expanding de Sitter space during this period.