Hamiltonian structure of scalar-tensor theories beyond Horndeski

TL;DR

This paper analyzes the Hamiltonian structure of a recent scalar-tensor gravity theory beyond Horndeski, confirming it maintains three degrees of freedom and is free from extra modes in a specific case.

Contribution

It provides a detailed Hamiltonian analysis of the GLPV scalar-tensor theory, establishing the number of degrees of freedom and confirming its consistency beyond Horndeski.

Findings

The theory has three physical degrees of freedom.

In the case A_5=0, the theory is free of extra degrees of freedom.

The Hamiltonian analysis confirms the theory's consistency at nonlinear level.

Abstract

We study the nature of constraints and the Hamiltonian structure in a scalar-tensor theory of gravity recently proposed by Gleyzes, Langlois, Piazza and Vernizzi (GLPV). For the simple case with A_5 = 0, namely when the canonical momenta conjugate to the spatial metric are linear in the extrinsic curvature, we prove that the number of physical degrees of freedom is three at fully nonlinear level, as claimed by GLPV. Therefore, while this theory extends Horndeski's scalar-tensor gravity theory, it is protected against additional degrees of freedom.