Braneworld gravity: Influence of the moduli fields

TL;DR

This paper derives the effective gravitational equations on a braneworld with multiple moduli fields, revealing novel modifications to stress-energy conservation, gravity couplings, and cosmological constant behavior in various frames and dimensions.

Contribution

It provides a comprehensive derivation of on-brane gravitational equations considering arbitrary moduli fields, curvature couplings, and dimensions, extending previous braneworld models.

Findings

Modified stress-energy conservation laws on the brane.

Anomalous couplings between gravity and stress-energy trace.

Additional mechanisms for altering the effective cosmological constant.

Abstract

We consider the case of a generic braneworld geometry in the presence of one or more moduli fields (e.g., the dilaton) that vary throughout the bulk spacetime. Working in an arbitrary conformal frame, using the generalized junction conditions of gr-qc/0008008 and the Gauss--Codazzi equations, we derive the effective ``induced'' on-brane gravitational equations. As usual in braneworld scenarios, these equations do not form a closed system in that the bulk can exchange both information and stress-energy with the braneworld. We work with an arbitrary number of moduli fields described by an arbitrary sigma model, with arbitrary curvature couplings, arbitrary self interactions, and arbitrary dimension for the bulk. (The braneworld is always codimension one.) Among the novelties we encounter are modifications of the on-brane stress-energy conservation law, anomalous couplings between on-brane gravity and the trace of the on-brane stress-energy tensor, and additional possibilities for modifying the on-brane effective cosmological constant. After obtaining the general stress-energy ``conservation'' law and the ``induced Einstein equations'' we particularize the discussion to two particularly attractive cases: for a (n-2)-brane in ([n-1]+1) dimensions we discuss both the effect of (1) generic variable moduli fields in the Einstein frame, and (2) the effect of a varying dilaton in the string frame.