A new instability in clustering dark energy?

TL;DR

This paper uncovers a new non-linear instability in the effective field theory of dark energy models with low sound speed, challenging the validity of linear approximations in these regimes.

Contribution

It identifies a previously unknown instability at next-to-leading order in EFT of dark energy, especially relevant for models with very low sound speed.

Findings

Instability arises at quadratic order in EFT equations of motion.

Singularity develops in finite time when sound speed vanishes.

Linear treatment is insufficient for a broad range of sound speeds.

Abstract

In this paper, we study the effective field theory (EFT) of dark energy for the $k$-essence model beyond linear order. Using particle-mesh $N$-body simulations that consistently solve the dark energy evolution on a grid, we find that the next-to-leading order in the EFT expansion, which comprises the terms of the equations of motion that are quadratic in the field variables, gives rise to a new instability in the regime of low speed of sound (high Mach number). We rule out the possibility of a numerical artefact by considering simplified cases in spherically and plane symmetric situations analytically. If the speed of sound vanishes exactly, the non-linear instability makes the evolution singular in finite time, signalling a breakdown of the EFT framework. The case of finite (but small) speed of sound is subtle, and the local singularity could be replaced by some other type of behaviour with strong non-linearities. While an ultraviolet completion may cure the problem in principle, there is no reason why this should be the case in general. As a result, for a large range of the effective speed of sound $c_s$, a linear treatment is not adequate.