A geometrical approach to degenerate scalar-tensor theories

TL;DR

This paper presents a geometric framework for degenerate scalar-tensor theories of gravity, linking them to DBI Galileons, analyzing their stability, and exploring dualities and symmetry-breaking mechanisms.

Contribution

It introduces a geometric approach to degenerate scalar-tensor systems, connects them to DBI Galileons, and explores their dualities and stability properties.

Findings

Some theories emerge as limits of DBI Galileons.

Breaking symmetry or coupling to gravity can address fluctuation propagation issues.

Distinct theories are connected via a generalized Galileon duality.

Abstract

Degenerate scalar-tensor theories are recently proposed covariant theories of gravity coupled with a scalar field. Despite being characterised by higher order equations of motion, they do not propagate more than three degrees of freedom, thanks to the existence of constraints. We discuss a geometrical approach to degenerate scalar-tensor systems, and analyse its consequences. We show that some of these theories emerge as a certain limit of DBI Galileons. In absence of dynamical gravity, these systems correspond to scalar theories enjoying a symmetry which is different from Galileon invariance. The scalar theories have however problems concerning the propagation of fluctuations around a time dependent background. These issues can be tamed by breaking the symmetry by hand, or by minimally coupling the scalar with dynamical gravity in a way that leads to degenerate scalar-tensor systems. We show that distinct theories can be connected by a relation which generalizes Galileon duality, in certain cases also when gravity is dynamical. We discuss some implications of our results in concrete examples. Our findings can be helpful for assessing stability properties and understanding the non-perturbative structure of systems based on degenerate scalar-tensor systems.