Covariant power-counting renormalizable gravity: Lorentz symmetry breaking and accelerating early-time FRW universe

TL;DR

This paper explores a covariant, power-counting renormalizable gravity theory with Lorentz symmetry breaking, proposing vector gravity models that admit inflationary solutions and black hole solutions, advancing quantum gravity research.

Contribution

It introduces a covariant vector gravity model with U(1) symmetry and analyzes its cosmological and black hole solutions, including dispersion relations for gravitons.

Findings

Existence of power-law and de Sitter inflationary solutions.

Derivation of black hole solutions within the model.

Presentation of graviton dispersion relations.

Abstract

We continue the study of covariant power-counting renormalizable gravity constrained by scalar Lagrange multiplier. Lorentz symmetry breaking is investigated in such a theory in comparison with the one in ghost condensation model. Covariant power-counting renormalizable vector gravity which is invariant under $U(1)$ gauge symmetry is proposed. Several forms of vector Lagrange multiplier in this theory are discussed. It is shown that covariant scalar/vector gravity under consideration may have power-law or de Sitter accelerating cosmological solution corresponding to inflationary era. Simplest black hole solution is obtained and dispersion relations for graviton are presented.