Geometries with mismatched branes

TL;DR

This paper explores time-dependent solutions in Randall-Sundrum two-brane models with mismatched tensions, revealing new cosmological scenarios described by an effective action involving the brane metric and radion field.

Contribution

It introduces a class of time-dependent solutions for mismatched brane tensions and formulates an effective action approach to describe these geometries.

Findings

Solutions can be succinctly described by an effective action involving the brane metric and radion.

Time-dependent solutions exist for mismatched brane tensions, potentially addressing cosmological issues.

Full geometries may require multiple coordinate patches for accurate description.

Abstract

We study Randall-Sundrum two brane setups with mismatched brane tensions. For the vacuum solutions, boundary conditions demand that the induced metric on each of the branes is either de Sitter, Anti-de Sitter, or Minkowski. For incompatible boundary conditions, the bulk metric is necessarily time-dependent. This introduces a new class of time-dependent solutions with the potential to address cosmological issues and provide alternatives to conventional inflationary (or contracting) scenarios. We take a first step in this paper toward such solutions. One important finding is that the resulting solutions can be very succinctly described in terms of an effective action involving only the induced metric on either one of the branes and the radion field. But the full geometry cannot necessarily be simply described with a single coordinate patch. We concentrate here on the time-dependent solutions but argue that supplemented with a brane stabilization mechanism one can potentially construct interesting cosmological models this way. This is true both with and without a brane stabilization mechanism.