On the stability conditions for theories of modified gravity in presence of matter fields

TL;DR

This paper provides a comprehensive stability analysis of modified gravity theories with matter, establishing viability conditions to avoid ghosts, gradient, and tachyonic instabilities within an effective field theory framework.

Contribution

It introduces a general stability criterion for modified gravity theories with matter, including beyond Horndeski models, using the EFT approach and Sorkin-Schutz action.

Findings

Ghost absence requires positive kinetic matrix

Scalar mode propagation speeds depend on matter density

Tachyonic instabilities occur when negative mass eigenvalues exceed Hubble scale

Abstract

We present a thorough stability analysis of modified gravity theories in the presence of matter fields. We use the Effective Field Theory framework for Dark Energy and Modified Gravity to retain a general approach for the gravity sector and a Sorkin-Schutz action for the matter one. Then, we work out the proper viability conditions to guarantee in the scalar sector the absence of ghosts, gradient and tachyonic instabilities. The absence of ghosts can be achieved by demanding a positive kinetic matrix, while the lack of a gradient instability is ensured by imposing a positive speed of propagation for all the scalar modes. In case of tachyonic instability, the mass eigenvalues have been studied and we work out the appropriate expressions. For the latter, an instability occurs only when the negative mass eigenvalue is much larger, in absolute value, than the Hubble parameter. We discuss the results for the minimally coupled quintessence model showing for a particular set of parameters two typical behaviours which in turn lead to a stable and an unstable configuration. Moreover, we find that the speeds of propagation of the scalar modes strongly depend on matter densities, for the beyond Horndeski theories. Our findings can be directly employed when testing modified gravity theories as they allow to identify the correct viability space.