NEC violation in mimetic cosmology revisited

TL;DR

This paper critically examines the possibility of NEC violation in mimetic cosmology, revealing inherent instabilities linked to the Einstein-Hilbert term and discussing potential resolutions.

Contribution

It demonstrates that mimetic cosmology is susceptible to gradient instabilities even when NEC is satisfied, challenging claims of stable NEC violation.

Findings

Mimetic cosmology exhibits gradient instabilities due to the Einstein-Hilbert term.

Matter stress-energy does not contribute to spatial gradient terms.

Mimetic theory is a singular limit of higher-derivative theories with potential instability remedies.

Abstract

In the context of Einstein gravity, if the null energy condition (NEC) is satisfied, the energy density in expanding space-times always decreases while in contracting space-times the energy density grows and the universe eventually collapses into a singularity. In particular, no non-singular bounce is possible. It is, though, an open question if this energy condition can be violated in a controlled way, i.e., without introducing pathologies, such as unstable negative-energy states or an imaginary speed of sound. In this paper, we will re-examine the claim that the recently proposed mimetic scenario can violate the NEC without pathologies. We show that mimetic cosmology is prone to gradient instabilities even in cases when the NEC is satisfied (except for trivial examples). Most interestingly, the source of the instability is always the Einstein-Hilbert term in the action. The matter stress-energy component does not contribute spatial gradient terms but instead makes the problematic curvature modes dynamical. We also show that mimetic cosmology can be understood as a singular limit of known, well-behaved theories involving higher-derivative kinetic terms and discuss ways of removing the instability.