Brane Induced Gravity, its Ghost and the Cosmological Constant Problem

TL;DR

This paper analyzes brane induced gravity models, highlighting ghost instabilities, their implications for the cosmological constant problem, and exploring the effects of background curvature and additional terms on the model's properties.

Contribution

It provides a detailed gauge-invariant analysis of codimension > 2 brane models, examining ghost issues, graviton properties, and the spontaneous breaking of covariance in a flat background approximation.

Findings

Ghost instability persists unless specific conditions are met.

The graviton propagator reveals a mass, decay width, and modified coupling.

Spontaneous breaking of covariance suggests a gravitational Higgs mechanism.

Abstract

"Brane Induced Gravity" is regarded as a promising framework for addressing the cosmological constant problem, but it also suffers from a ghost instability for parameter values that make it phenomenologically viable. We carry out a detailed analysis of codimension > 2 models employing gauge invariant variables in a flat background approximation. It is argued that using instead a curved background sourced by the brane would not resolve the ghost issue, unless a very specific condition is satisfied (if satisfiable at all). As for other properties of the model, from an explicit analysis of the 4-dimensional graviton propagator we extract a mass, a decay width and a momentum dependent modification of the gravitational coupling for the spin 2 mode. In the flat space approximation, the mass of the problematic spin 0 ghost is instrumental in filtering out a brane cosmological constant. The mass replaces a background curvature that would have had the same function. The optical theorem is used to demonstrate the suppression of graviton leakage into the uncompactified bulk. Then, we derive the 4-dimensional effective action for gravity and show that general covariance is spontaneously broken by the bulk-brane setup. This provides a natural realization of the gravitational Higgs mechanism. We also show that the addition of extrinsic curvature dependent terms has no bearing on linearized brane gravity.