Degravitation Features in the Cascading Gravity Model

TL;DR

This paper derives effective gravitational equations in the cascading gravity model, explores cosmological solutions, and demonstrates the model's potential for degravitation of the cosmological constant, highlighting stability conditions.

Contribution

It provides a new formulation for effective gravitational equations in cascading gravity, including cosmological solutions with matter on the branes, and analyzes stability and degravitation features.

Findings

Cascading gravity exhibits degravitation of the cosmological constant.

Only certain solution branches satisfy the null energy condition.

Effective Friedmann equations are derived for the codimension-2 brane.

Abstract

We obtain the effective gravitational equations on the codimension-2 and codimension-1 branes in the cascading gravity model. We then apply our formulation to the cosmological case and obtain the effective Friedmann equations on the codimension-2 brane, which are generically given in terms of integro-differential equations. Adopting an approximation for which the thickness of the codimension-2 brane is much smaller than the Hubble horizon, we study the Minkowski and de Sitter codimension-2 brane solutions. Studying the cosmological solutions shows that the cascading model exhibits the features necessary for degravitation of the cosmological constant. We also show that only the branch which does not have the smooth limit to the self-accelerating branch in five-dimensional model in the absence of the bulk gravity can satisfy the null energy condition as the criterion of the stability. Note that our solutions are obtained in a different setup from that of the original cascading gravity model in the sense that the codimension-1 brane contains matter fields other than the pure tension.