Gravity from spontaneous Lorentz violation

TL;DR

This paper explores a gravity theory derived from spontaneous Lorentz symmetry breaking, showing it reproduces general relativity at low energies but differs at high energies, with potential observable effects.

Contribution

It introduces a nonlinear gravity theory from spontaneous Lorentz violation, linking Nambu-Goldstone modes to Einstein equations and proposing an alternative to general relativity.

Findings

Reproduces Einstein gravity at low energies

Differs from general relativity at high energies

Predicts observable effects in gravitational experiments

Abstract

We investigate a class of theories involving a symmetric two-tensor field in Minkowski spacetime with a potential triggering spontaneous violation of Lorentz symmetry. The resulting massless Nambu-Goldstone modes are shown to obey the linearized Einstein equations in a fixed gauge. Imposing self-consistent coupling to the energy-momentum tensor constrains the potential for the Lorentz violation. The nonlinear theory generated from the self-consistent bootstrap is an alternative theory of gravity, containing kinetic and potential terms along with a matter coupling. At energies small compared to the Planck scale, the theory contains general relativity, with the Riemann-spacetime metric constructed as a combination of the two-tensor field and the Minkowski metric. At high energies, the structure of the theory is qualitatively different from general relativity. Observable effects can arise in suitable gravitational experiments.