Effective Gravitational Equations on Brane World with Induced Gravity

TL;DR

This paper derives effective four-dimensional gravitational equations for brane world models with induced gravity, showing that the effective cosmological constant can be naturally small without fine-tuning, extending the Dvali-Gabadadze-Porrati model.

Contribution

The paper develops a formalism for effective gravitational equations on a brane with induced gravity, generalizing previous models and demonstrating a mechanism for small effective cosmological constant.

Findings

Effective equations for brane gravity derived from 5D Einstein equations.

In the generalized model, the brane cosmological constant can be significantly reduced.

The reduction occurs without fine-tuning of bulk cosmological constant or brane tension.

Abstract

We present the effective equations to describe the four-dimensional gravity of a brane world, assuming that a five-dimensional bulk spacetime satisfies the Einstein equations and gravity is confined on the $Z_2$ symmetric brane. Applying this formalism, we study the induced-gravity brane model first proposed by Dvali, Gabadadze and Porrati. In a generalization of their model, we show that an effective cosmological constant on the brane can be extremely reduced in contrast to the case of the Randall-Sundrum model even if a bulk cosmological constant and a brane tension are not fine-tuned.