Propagation of anisotropic gravitational and electromagnetic waves at very high energies

TL;DR

This paper investigates the propagation of anisotropic gravitational and electromagnetic waves at very high energies within a Hořava-Lifshitz inspired model, revealing unique dispersion relations and stability properties that differ from LIV models.

Contribution

It introduces a new anisotropic gravity-electromagnetic theory based on Hořava-Lifshitz principles, analyzing its dispersion relation and stability at high energies.

Findings

The model's wave equation matches relativistic form at lowest order.

It identifies the exact propagation zone for physical degrees of freedom.

Predictions differ from LIV models for high-energy photon propagation.

Abstract

We analyze the dispersion relation for an anisotropic gravity-electromagnetic theory at very high energies. In particular for photons of very high energy. We start by introducing the anisotropic gravity-gauge vector field model. It is invariant under spacelike diffeomorphisms, time parametrization, and U(1) gauge transformations. It includes high-order spacelike derivatives as well as polynomial expressions of the Riemann and field strength tensor fields. It is based on the Ho\v{r}ava-Lifshitz anisotropic proposal. We show its consistency, and the stability of the Minkowski ground state. Finally, we determine the exact zone at which the physical degrees of freedom, i.e. the transverse-traceless tensorial degrees of freedom and the transverse vectorial degrees of freedom propagate according to a linear wave equation. This is so, in spite of the fact that there exists in the zone a non-trivial Newtonian background of the same order. The wave equation contains spatial derivatives up to the sixth order, in the lowest order it exactly matches the relativistic wave equation. We then analyze the dispersion relation at very high energies in the context of recent experimental data. The qualitative predictions of the proposed model, concerning the propagation of highly energetic photons, are different from the ones obtained from the modified dispersion relation of the LIV models.