Relation between general relativity and a class of Horava gravity theories

Violations of Lorentz (and specifically boost) invariance can make gravity renormalizable in the ultraviolet, as initially noted by Horava, but are increasingly constrained in the infrared. At low energies, Horava gravity is characterized by three dimensionless couplings, alpha, beta and lambda, which vanish in the general relativistic limit. Solar system and gravitational wave experiments bound two of these couplings (alpha and beta) to tiny values, but the third remains relatively unconstrained (0 <= lambda less than or similar to 0.01-0.1). Moreover, demanding that (slowly moving) black-hole solutions are regular away from the central singularity requires alpha and beta to vanish exactly. Although a canonical constraint analysis shows that the class of khronometric theories resulting from these constraints (alpha = beta = 0 and lambda not equal 0) cannot be equivalent to General Relativity, even in vacuum, previous calculations of the dynamics of the solar system, binary pulsars and gravitational-wave generation show perfect agreement with general relativity. Here, we analyze spherical collapse and compute black-hole quasinormal modes, and find again that they behave exactly as in general relativity, as far as observational predictions are concerned. Nevertheless, we find that spherical collapse leads to the formation of a regular universal horizon, i.e., a causal boundary for signals of arbitrary propagation speeds, inside the usual event horizon for matter and tensor gravitons. Our analysis also confirms that the additional scalar degree of freedom present alongside the spin-2 graviton of general relativity remains strongly coupled at low energies, even on curved backgrounds. These puzzling results suggest that any further bounds on Horava gravity will probably come from cosmology.

Automated summary

Violations of Lorentz invariance can lead to gravity becoming renormalizable in the UV, as observed by Horava, but are increasingly constrained in the IR. Experimental bounds suggest that Horava gravity is consistent with general relativity in many aspects, but there are puzzling discrepancies that may require further investigation, possibly from a cosmological perspective.