Caustic Formation upon Shift Symmetry Breaking

TL;DR

This paper investigates how breaking shift symmetry influences caustic formation in canonical, DBI, and conformal Galileon theories, revealing that caustic formation depends on the specific model and symmetry considerations.

Contribution

It demonstrates that shift symmetry breaking affects caustic formation differently across models and discusses the invariance of simple wave conditions under field redefinitions.

Findings

Canonical kinetic theory remains caustic free after symmetry breaking.

DBI theory can develop caustics when shift symmetry is broken.

Simple wave conditions are not invariant under field redefinitions.

Abstract

We examine how the breaking of shift symmetry affects the formation of caustics for the standard canonical kinetic theory as well as for the DBI theory. We show in this case, that the standard canonical kinetic theory is caustic free but the same does not always apply for the DBI model. We make similar arguments about the conformal Galileons. Finally, it is shown that the simple wave condition is not invariant under field redefinitions and the meaning of simple waves after symmetry breaking is discussed.