Formation of caustics in k-essence and Horndeski theory

TL;DR

This paper investigates wave propagation in k-essence and Horndeski theories, revealing that generic initial conditions lead to caustic formation, which has significant physical implications and challenges for these models.

Contribution

It demonstrates that caustic formation is a generic feature in k-essence and Horndeski theories, extending previous solutions and analyzing physical consequences.

Findings

Generic initial conditions lead to caustic formation in k-essence.

Traveling wave solutions are fine-tuned and not generic.

Caustic formation occurs in the broader class of Horndeski theories with k-essence.

Abstract

We study propagation of waves and appearance of caustics in k-essence and galileon theories. First we show that previously known solutions for travelling waves in k-essence and galileon models correspond to very specific fine-tuned initial conditions. On the contrary, as we demonstrate by the method of characteristics, generic initial conditions leads to a wave in k-essence which ends up with formation of caustics. Finally, we find that any wave solution in pure k-essence is also a solution for a galileon theory with the same k-essence term. Thus in the Horndeski theory with a k-essence term formation of caustics is generic. We discuss physical consequences of the caustics formation and possible ways to cure the problem.