Dilaton-gravity on the brane

TL;DR

This paper derives the effective four-dimensional equations for a brane-world scenario with a scalar field in the bulk, analyzing gravitational and cosmological implications including static and dynamic solutions.

Contribution

It provides a comprehensive derivation of the 4D field equations for a brane with a scalar field in the bulk, including effective constants and cosmological solutions.

Findings

Derived effective 4D gravitational and cosmological constants.

Presented static Minkowski and dynamic FRW brane solutions.

Analyzed scalar field coupling to matter on the brane.

Abstract

We derive the four-dimensional field equations for the induced metric and scalar field on the world-volume of a 3-brane in a five-dimensional bulk with Einstein gravity plus a self-interacting scalar field. We calculate the effective four-dimensional gravitational constant and cosmological constant for arbitrary forms of the brane tension and self-interaction potential for the scalar field in the bulk. In addition to the canonical energy-momentum tensor for the scalar field and ordinary matter on the brane, the effective four-dimensional Einstein equations include terms due to the scalar field and gravitational waves in the bulk. We present solutions corresponding to static Minkowski brane worlds and also dynamical Friedmann-Robertson-Walker brane world cosmologies. We discuss the induced coupling of the scalar field to ordinary matter on the brane.