Degenerate Horava gravity

Abstract

Horava gravity breaks Lorentz symmetry by introducing a dynamical timelike scalar field (the khronon), which can be used as a preferred time coordinate (thus selecting a preferred space-time foliation). Adopting the khronon as the time coordinate, the theory is invariant only under time reparametrizations and spatial diffeomorphisms. In the infrared limit, this theory is sometimes referred to as khronometric theory. Here, we explicitly construct a generalization of khronometric theory, which avoids the propagation of Ostrogradski modes as a result of a suitable degeneracy condition (although stability of the latter under radiative corrections remains an open question). While this new theory does not have a general-relativistic limit and does not yield a Friedmann-Robertson-Walker-like cosmology on large scales, it still passes, for suitable choices of its coupling constants, local tests on Earth and in the solar system, as well as gravitational-wave tests. We also comment on the possible usefulness of this theory as a toy model of quantum gravity, as it could be completed in the ultraviolet into a 'degenerate Horava gravity' theory that could be perturbatively renormalizable without imposing any projectability condition.

19 pages, no figures; Comments on the stability under quantum corrections amended in v2; CQG version

References in corpus (7)

• The Confrontation between General Relativity and Experiment
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• Quantum Gravity at a Lifshitz Point
• Healthy theories beyond Horndeski
• Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
• Models of non-relativistic quantum gravity: the good, the bad and the healthy
• On the Extra Mode and Inconsistency of Horava Gravity