Massive Gravity in Curved Cosmological Backgrounds

TL;DR

This paper investigates a massive gravity model in curved cosmological backgrounds, demonstrating the absence of ghosts and instabilities, with tensor modes acquiring mass and scalar sectors breaking Lorentz invariance but remaining healthy.

Contribution

It provides a detailed analysis of propagating modes in a massive gravity model on curved backgrounds, confirming stability and absence of Boulware-Deser ghosts under ghost condensation assumptions.

Findings

No scalar ghost or tachyon in the spectrum

Tensor modes become massive via gravitational Higgs mechanism

Scalar sector breaks Lorentz invariance without pathologies

Abstract

We study the physical propagating modes in a massive gravity model in curved cosmological backgrounds, which we have found as classical solutions in our previous paper. We show that, generically, there exist such the cosmological background solutions consistent with the equations of motion where we assume the ghost condensation ansatzes. Using the (1+3)-parametrization of the metric fluctuations with 'unitary' gauge, we find that there is neither a scalar ghost nor a tachyon in the spectrum of the propagating modes, the tensor modes become massive owing to gravitational Higgs mechanism, and the model is free of the Boulware-Deser instability. The price we have to pay is that the scalar sector breaks the Lorentz-invariance, but there are no pathologies in the spectrum and lead to interesting phenomenology. Moreover, we present a proof of the absence of non-unitary modes for a specific ghost condensation model in a cosmological background.