Stability of Geodesically Complete Cosmologies

TL;DR

This paper analyzes the stability of geodesically complete, NEC-violating cosmologies like smooth bounces, highlighting the role of specific operators in avoiding gradient instabilities within the effective field theory framework.

Contribution

It identifies the critical operator in the EFT that prevents gradient instabilities in geodesically complete cosmologies, emphasizing its unique properties and limitations.

Findings

Gradient instability can be avoided with the operator $~^{(3)}{R} abla N$

This operator is characteristic of beyond-Horndeski theories

Sign change of the operator prevents setting it to zero via disformal transformations

Abstract

We study the stability of spatially flat FRW solutions which are geodesically complete, i.e. for which one can follow null (graviton) geodesics both in the past and in the future without ever encountering singularities. This is the case of NEC-violating cosmologies such as smooth bounces or solutions which approach Minkowski in the past. We study the EFT of linear perturbations around a solution of this kind, including the possibility of multiple fields and fluids. One generally faces a gradient instability which can be avoided only if the operator $~^{(3)}{R} \delta N~$ is present and its coefficient changes sign along the evolution. This operator (typical of beyond-Horndeski theories) does not lead to extra degrees of freedom, but cannot arise starting from any theory with second-order equations of motion. The change of sign of this operator prevents to set it to zero with a generalised disformal transformation.