Null energy condition and superluminal propagation

TL;DR

This paper investigates the relationship between null energy condition violations and instabilities, showing that while violations often lead to instabilities, there are stable counter-examples with superluminal modes and anisotropy.

Contribution

The paper demonstrates that null energy condition violations do not always imply instabilities, highlighting the role of anisotropy and superluminal modes in stable theories.

Findings

Violations of the null energy condition often lead to instabilities.

Counter-examples exist with stable backgrounds violating the null energy condition.

Superluminal modes and anisotropy are key features of stable violations.

Abstract

We study whether a violation of the null energy condition necessarily implies the presence of instabilities. We prove that this is the case in a large class of situations, including isotropic solids and fluids relevant for cosmology. On the other hand we present several counter-examples of consistent effective field theories possessing a stable background where the null energy condition is violated. Two necessary features of these counter-examples are the lack of isotropy of the background and the presence of superluminal modes. We argue that many of the properties of massive gravity can be understood by associating it to a solid at the edge of violating the null energy condition. We briefly analyze the difficulties of mimicking $\dot H>0$ in scalar tensor theories of gravity.