A new nonlinear instability for scalar fields

TL;DR

This paper introduces a new nonlinear PDE instability relevant to dark energy models, demonstrating its occurrence in cosmological simulations and analyzing its mathematical properties in spherical symmetry.

Contribution

It presents a novel nonlinear instability in scalar field equations, relevant to EFT of dark energy, with both numerical and analytical investigations.

Findings

The instability dominates at low sound speeds.

Numerical simulations confirm the instability in cosmological models.

Mathematical analysis in spherical symmetry elucidates the instability mechanism.

Abstract

In this letter we introduce the non-linear partial differential equation (PDE) $\partial^2_{\tau} \pi \propto (\vec\nabla \pi)^2$ showing a new type of instability. Such equations appear in the effective field theory (EFT) of dark energy for the $k$-essence model as well as in many other theories based on the EFT formalism. We demonstrate the occurrence of instability in the cosmological context using a relativistic $N$-body code, and we study it mathematically in 3+1 dimensions within spherical symmetry. We show that this term dominates for the low speed of sound limit where some important linear terms are suppressed.