Hamiltonian structure of scalar-tensor theories beyond Horndeski

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.

11 pages

References in corpus (6)

• Covariant Galileon
• Unifying framework for scalar-tensor theories of gravity
• Effective field theory of modified gravity with two scalar fields: dark energy and dark matter
• The effective field theory of inflation/dark energy and the Horndeski theory
• Cosmology in generalized Horndeski theories with second-order equations of motion
• Effective field theory of modified gravity on the spherically symmetric background: leading order dynamics and the odd-type perturbations

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• Fundamental theorem on gauge fixing at the action level
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• Spatially covariant gravity: Perturbative analysis and field transformations
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