Matter coupling in partially constrained vielbein formulation of massive gravity

Antonio De Felice,Shinji Mukohyama,Lavinia Heisenberg,A Emir Gümrükçüoğ

doi:10.1088/1475-7516/2016/01/003

Abstract

We consider a 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.

Highlights

The above mentioned difficulties in the cosmological setup arise only in the case of the minimal coupling to one of the metrics, which can be avoided by considering a matter coupling through a very specific admixture of the dynamical and fiducial metric [27]
The mass of the Boulware-Deser ghost on the FLRW background is infinite. This is because the ghostly vector-scalar-matter interactions do not contribute to the background due to the symmetry of FLRW
The question of consistent matter couplings within the framework of massive gravity is crucial for maintaining the ghost freedom

Summary

MPl s 0

Using the solutions of these equations reduces the action to contain three degrees of freedom only. In the regime where the matter sector is parametrically subdominant under the mass term, the second eigenvalue gives a condition reminiscent of Higuchi bound, i.e. m2 J(m2 J A −. This choice of basis is just convenience since the subhorizon limit of the kinetic term turns out to be of order k 0. If the fiducial metric is maximally symmetric, this gives a new relation between J and the matter components. For this example, the second kinetic eigenvalue is κ2

MPl α β a2eff ρ

Conclusions