Is the DBI scalar field as fragile as other $k$-essence fields?

TL;DR

This paper investigates caustic singularities in shift-symmetric $k$-essence and Horndeski theories, finding that the DBI scalar and canonical scalar are free from such singularities under planar symmetry, challenging previous claims.

Contribution

The study demonstrates that the DBI scalar, along with the canonical scalar, avoids caustic singularities in simple wave solutions, even with Horndeski terms, contrary to earlier assertions.

Findings

DBI scalar is free from caustic singularities under planar symmetry.

Canonical scalar also avoids caustics in this setting.

Adding Horndeski terms does not induce caustics in simple wave solutions.

Abstract

Caustic singularity formations in shift-symmetric $k$-essence and Horndeski theories on a fixed Minkowski spacetime were recently argued. In $n$ dimensions, this singularity is the $(n-2)$-dimensional plane in spacetime at which second derivatives of a field diverge and the field loses single-valued description for its evolution. This does not necessarily imply a pathological behavior of the system but rather invalidates the effective description. The effective theory would thus have to be replaced by another to describe the evolution thereafter. In this paper, adopting the planar-symmetric $1$+$1$-dimensional approach employed in the original analysis, we seek all $k$-essence theories in which generic simple wave solutions are free from such caustic singularities. Contrary to the previous claim, we find that not only the standard canonical scalar but also the DBI scalar are free from caustics, as far as planar-symmetric simple wave solutions are concerned. Addition of shift-symmetric Horndeski terms does not change the conclusion.