Year: 2019
Type: article
Abstract: Minimally modified gravity theories are modifications of general relativity with two local gravitational degrees of freedom in four dimensions. Their construction relies on the breaking of 4D diffeomorphism invariance keeping however the symmetry under 3D diffeomorphisms. Here, we construct these theories from the Hamiltonian point of view. We start with the phase space of general relativity in the ADM formalism. Then, we find the conditions that the Hamiltonian must satisfy for the theory to propagate (up to) two local gravitational degrees of freedom with the assumptions that the lapse and the shift are not dynamical, and that the theory remains invariant under 3D diffeomorphisms. This construction enables us to recover the well-known "cuscuton" class of scalar-tensor theories in the unitary gauge. We also exhibit a new class of interesting theories, that we dub f ( ) theories, where the usual Hamiltonian constraint of general relativity is replaced by f ( ) where f is an arbitrary function.
Authors: S. Mukohyama, K. Noui
Institutions: Kavli Institute for the Physics and Mathematics of the Universe, Kyoto University, Yukawa Institute for Theoretical Physics, The University of Tokyo, Université de Tours, Université d'Orléans, Centre National de la Recherche Scientifique, Laboratoire AstroParticule et Cosmologie, Université Paris Diderot, Institut Denis Poisson
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2943206952