Asymmetric brane-worlds with induced gravity

TL;DR

This paper explores asymmetric brane-world models with induced gravity, deriving the governing equations and analyzing their effects on cosmological dynamics, especially in Friedmann branes within anti-de Sitter bulk.

Contribution

It generalizes the Randall-Sundrum model by relaxing Z2-symmetry and including induced gravity, providing a complete set of equations and solutions for these extended scenarios.

Findings

Asymmetry and induced gravity act as effective sources in brane equations.

Solutions for Friedmann equations involve quartic equations.

Perturbative analysis shows late-time effects of asymmetry.

Abstract

The Randall-Sundrum scenario, with a 1+3-dimensional brane in a 5-dimensional bulk spacetime, can be generalized in various ways. We consider the case where the Z2-symmetry at the brane is relaxed, and in addition the gravitational action is generalized to include an induced gravity term on the brane. We derive the complete set of equations governing the gravitational dynamics for a general brane and bulk, and identify how the asymmetry and the induced gravity act as effective source terms in the projected field equations on the brane. For a Friedmann brane in an anti de Sitter bulk, the solution of the Friedmann equation is given by the solution of a quartic equation. We find the perturbative solutions for small asymmetry, which has an effect at late times.