Braneworld sum rules and positive tension branes in a massive gravity

TL;DR

This paper investigates the construction of flat 3-brane models with only positive tension branes within a 5D Lorentz-violating massive gravity framework, addressing key cosmological and hierarchy issues while analyzing perturbation spectra.

Contribution

It demonstrates the feasibility of positive tension-only brane configurations in a massive gravity setting and explores their perturbative stability and phenomenology.

Findings

Supported three brane configurations, including a positive tension-only scenario.

Solved the cosmological and hierarchy problems simultaneously.

Found that tensor, vector, and scalar modes are massive with specific spectral properties.

Abstract

By taking advantage of the braneworld sum rules, we explore the feasibility of constructing a flat 3-brane scenario consisting solely of positive tension branes in a 5D extension of the Lorentz-violating massive gravity. It is found that the theory supports three distinct brane configurations, one of which is exactly what we expected, consisting solely of two positive tension branes. The cosmological problem of Randall-Sundrum-1 model and the gauge hierarchy problem can be solved in this model simultaneously. Furthermore, the analysis of linear perturbations reveals that the tensor, vector and scalar modes are all massive and share the same mass spectrum, except that the ground state of vector mode is absent. Moreover, the tensor and vector modes are robust, but the scalar mode is ghost-like. Interestingly, even though the Kaluza-Klein gravitons have an extremely small mass splitting scale, an estimation of the effective gravitational potential and production of these gravitons on the brane indicates that the phenomenology of the present model is equivalent to that of the 6D ADD model.