Relativistic Gravity With a Dynamical Preferred Frame

TL;DR

The paper investigates whether gravity can accommodate Lorentz violation within a consistent effective field theory by introducing a dynamical preferred frame, the aether field $u^a$. It formalizes a covariant gravity–aether EFT with $L_{g,u}$ containing terms up to two derivatives and a Lagrange multiplier enforcing a unit constraint, enabling Lorentz breaking while preserving rotation; the matter sector is allowed to couple to the aether via Lorentz-violating terms. It then analyzes observational consequences across static-field solutions, Eötvös tests, gravitational waves, and cosmology, and identifies key viability issues such as energetic stability and potential shocks, outlining possible remedies (e.g., additional symmetric-derivative terms). The work provides a concrete, testable framework for Lorentz-violating gravity, offering predictions for solar-system tests, GW propagation, and early-universe phenomena, while underscoring the need for a positive-energy theorem and stability analyses to establish long-term viability.

Abstract

While general relativity possesses local Lorentz invariance, both canonical quantum gravity and string theory suggest that Lorentz invariance may be broken at high energies. Broken Lorentz invariance has also been postulated as an explanation for astrophysical anomalies such as the missing GZK cutoff. Therefore, we seek an effective field theory description of gravity where Lorentz invariance is broken. We will construct a candidate theory and then briefly discuss some of the implications.