Decaying Cosmological Constant of the Inflating Branes in the Randall-Sundrum -Oda Model

TL;DR

This paper investigates how the effective cosmological constant on inflating branes in the Randall-Sundrum-Oda model decays over time, showing that positive tension branes have a localized, decreasing cosmological constant due to their dynamics.

Contribution

It provides an exact solution in the slow roll approximation for the radion and demonstrates the decay of the cosmological constant on positive tension branes within this framework.

Findings

Positive tension branes have a localized, decaying cosmological constant.

The effective expansion rate depends on the brane's position in the fifth dimension.

Branes adjust their position in the fifth dimension to stabilize their expansion rate.

Abstract

We examine the issue of the cosmological constant in the $many$ $inflating$ branes scenario, extending on two recent models by I.Oda and Randall-Sundrum. The exact solution in a closed form is found in the slow roll approximation of the radion. Defining an effective expansion rate, which depends on the location of each brane in the fifth dimension and demanding stability for this case we show that each positive tension brane has a localized, decaying cosmological constant (the opposite process applies to the negative energy branes [4]) . The reason is that the square of the effective expansion rate enters as a source term in the Einstein equations for the branes.Thus the brane has two scale factors depending on time and the fifth dimnesion respectively .The brane will roll along the fifth dimension in order to readjust its effective expansion rate in such a way that it compensates for its internal energy changes due to inflation and possible phase transitions.