Matter coupling in partially constrained vielbein formulation of massive gravity

TL;DR

This paper introduces a ghost-free matter coupling in massive gravity using a partially constrained vielbein approach, analyzing its theoretical consistency and distinct cosmological perturbation features compared to metric formulations.

Contribution

It presents a novel ghost-free matter coupling in massive gravity within a partially constrained vielbein framework and explores its cosmological implications.

Findings

Ghost absence at all scales confirmed.

Tensor perturbations match metric formulation.

Different stability conditions for vector and scalar perturbations.

Abstract

We consider a consistent linear effective vielbein matter coupling without introducing the Boulware-Deser ghost in ghost-free massive gravity. This is achieved in the partially constrained vielbein formulation. We first introduce the formalism and prove the absence of ghost at all scales. As next we investigate the cosmological application of this coupling in this new formulation. We show that even if the background evolution accords with the metric formulation, the perturbations display important different features in the partially constrained vielbein formulation. We study the cosmological perturbations of the two branches of solutions separately. The tensor perturbations coincide with those in the metric formulation. Concerning the vector and scalar perturbations, the requirement of absence of ghost and gradient instabilities yields slightly different allowed parameter space.