Modified Dispersion Relations in Horava-Lifshitz Gravity and Finsler Brane Models

TL;DR

This paper explores the connections between quantum gravity phenomenology with Lorentz violations, Einstein-Finsler gravity models, and Hořava-Lifshitz theories, proposing covariant, integrable models that incorporate anisotropic deformations and potential quantization methods.

Contribution

It introduces covariant Einstein-Finsler gravity models and their anisotropic deformations as integrable, quantizable theories linking quantum gravity phenomenology with modified gravity frameworks.

Findings

Constructed covariant Einstein-Finsler gravity models on tangent bundles.

Demonstrated integrability and quantization approaches for these models.

Proposed mechanisms for recovering general relativity at large scales.

Abstract

We study possible links between quantum gravity phenomenology encoding Lorentz violations as nonlinear dispersions, the Einstein-Finsler gravity models, EFG, and nonholonomic (non-integrable) deformations to Ho\v{r}ava-Lifshitz, HL, and/or Einstein's general relativity, GR, theories. EFG and its scaling anisotropic versions formulated as Ho\v{r}ava-Finsler models, HF, are constructed as covariant metric compatible theories on (co) tangent bundle to Lorentz manifolds and respective anisotropic deformations. Such theories are integrable in general form and can be quantized following standard methods of deformation quantization, A-brane formalism and/or (perturbatively) as a nonholonomic gauge like model with bi-connection structure. There are natural warping/trapping mechanisms, defined by the maximal velocity of light and locally anisotropic gravitational interactions in a (pseudo) Finsler bulk spacetime, to four dimensional (pseudo) Riemannian spacetimes. In this approach, the HL theory and scenarios of recovering GR at large distances are generated by imposing nonholonomic constraints on the dynamics of HF, or EFG, fields.