Superluminality in beyond Horndeski theory with extra scalar field

TL;DR

This paper investigates superluminal propagation in beyond Horndeski theories with an extra scalar field, showing that superluminality occurs under certain conditions and constrains the theory's structure.

Contribution

It demonstrates that superluminal modes are unavoidable in beyond Horndeski theories with a minimally coupled scalar rolling, imposing new constraints on these models.

Findings

Superluminal propagation occurs when the scalar rolls, even slowly.

The result applies to all beyond Horndeski theories with six arbitrary functions.

Absence of superluminality constrains the theory's structure.

Abstract

We study the superluminality issue in beyond Horndeski theory with additional scalar field, which is minimally coupled to gravity and has no second derivatives in the Lagrangian. We present the quadratic action for perturbations in cosmological backgrounds, stability conditions and expressions for sound speeds. We find that in the case of conventional additional scalar whose flat-space propagation speed is that of light, one of the modes in interacting theory is necessarily superluminal when this scalar rolls, even arbitrarily slowly. This result holds in any theory of the beyond Horndeski class (with 6 arbitrary functions in the Lagrangian) and for any stable rolling background. More generally, the requirement of the absence of superluminality imposes non-trivial constraints on the structure of the theory.