Kaluza-Klein two-brane-worlds cosmology at low energy

TL;DR

This paper investigates low-energy cosmology in two-brane models within higher-dimensional spacetime, deriving effective scalar-tensor gravity and analyzing how internal dimensions' dynamics influence cosmological equations and dark radiation effects.

Contribution

It derives the effective $(4+n)$-dimensional scalar-tensor gravity from higher-dimensional brane models and explores the impact of static and nonstatic internal dimensions on cosmological evolution.

Findings

Effective gravitational constant depends on brane matter equations of state.

Dark radiation term naturally appears in the static internal dimensions case.

The relation $b(t)=a^eta(t)$ modifies Friedmann equations and affects dark radiation behavior.

Abstract

We study two $(4+n)$-dimensional branes embedded in $(5+n)$-dimensional spacetime. Using the gradient expansion approximation, we find that the effective theory is described by $(4+n)$-dimensional scalar-tensor gravity with a specific coupling function. Based on this theory we investigate the Kaluza-Klein two-brane-worlds cosmology at low energy, in both the static and the nonstatic internal dimensions. In the case of the static internal dimensions, the effective gravitational constant in the induced Friedmann equation depends on the equations of state of the brane matter, and the dark radiation term naturally appears. In the nonstatic case we take a relation between the external and internal scale factors of the form $b(t)=a^\gamma(t)$ in which the brane world evolves with two scale factors. In this case, the induced Friedmann equation on the brane is modified in the effective gravitational constant and the term proportional to $a^{-4\beta}$. For dark radiation, we find $\gamma=-2/(1+n)$. Finally, we discuss the issue of conformal frames which naturally arises with scalar-tensor theories. We find that the static internal dimensions in the Jordan frame may become nonstatic in the Einstein frame.