3+1 Formulation of the Standard-Model Extension Gravity Sector

TL;DR

This paper develops a 3+1 Hamiltonian formulation of the Standard-Model Extension's gravitational sector, revealing significant differences from General Relativity and exploring cosmological implications with modified Friedmann equations.

Contribution

It introduces a novel 3+1 Hamiltonian framework for the SME gravity sector with explicit symmetry breaking, and applies it to cosmology to derive modified Friedmann equations.

Findings

Significant differences from General Relativity in the dynamics.

Modified Friedmann equations with intriguing cosmological modifications.

Potential impacts on gravitational theory and phenomenology.

Abstract

We present a 3+1 formulation of the effective field theory framework called the Standard-Model Extension in the gravitational sector. The explicit local Lorentz and diffeomorphism symmetry breaking assumption is adopted and we perform a Dirac-Hamiltonian analysis. We show that the structure of the dynamics presents significant differences from General Relativity and other modified gravity models. We explore Hamilton's equations for some special choices of the coefficients. Our main application is cosmology and we present the modified Friedmann equations for this case. The results show some intriguing modifications to standard cosmology. In addition, we compare our results to existing frameworks and models and we comment on the potential impact to other areas of gravitational theory and phenomenology.