Cosmological Evolution of Brane World Moduli

TL;DR

This paper investigates how evolving moduli fields in five-dimensional brane world models with bulk scalars influence cosmology, deriving effective theories, and analyzing conditions for observational consistency and stability.

Contribution

It derives a bi-scalar-tensor effective theory from five dimensions and studies the cosmological evolution and attractor solutions of brane moduli.

Findings

Small alpha (less than 10^{-2}) is required for consistency with local gravity.

Attractor solutions can drive moduli to observationally acceptable values.

Negative tension brane approaches a bulk singularity, indicating limits of the 4D approximation.

Abstract

We study cosmological consequences of non-constant brane world moduli in five dimensional brane world models with bulk scalars and two boundary branes. We focus on the case where the brane tension is an exponential function of the bulk scalar field, $U_b \propto \exp{(\alpha \phi)}$. In the limit $\alpha \to 0$, the model reduces to the two-brane model of Randall-Sundrum, whereas larger values of $\alpha$ allow for a less warped bulk geometry. Using the moduli space approximation, we derive the four-dimensional low-energy effective action from a supergravity-inspired five-dimensional theory. For arbitrary values of $\alpha$, the resulting theory has the form of a bi-scalar-tensor theory. We show that, in order to be consistent with local gravitational observations, $\alpha$ has to be small (less than $10^{-2}$) and the separation of the branes must be large. We study the cosmological evolution of the interbrane distance and the bulk scalar field for different matter contents on each branes. Our findings indicate that attractor solutions exist which drive the moduli fields towards values consistent with observations. The efficiency of the attractor mechanism crucially depends on the matter content on each branes. In the five-dimensional description, the attractors correspond to the motion of the negative tension brane towards a bulk singularity, which signals the eventual breakdown of the four-dimensional description and the necessity of a better understanding of the bulk singularity.