# Lorentz-violating gravity and the bootstrap procedure

## TL;DR

This paper extends the bootstrap procedure to a Lorentz-violating gravity model, introducing a non-minimal coupling that differs from standard models at higher orders, with potential implications for anisotropic cosmologies.

## Contribution

It develops a Lorentz-violating gravity model using the bootstrap procedure, highlighting differences from known models at higher perturbative orders.

## Key findings

- Unobservable effects in FRW spacetimes
- Potential importance in anisotropic cosmologies
- Model resembles a generalized Proca theory with non-minimal coupling

## Abstract

In conventional gravitational physics, the so-called "bootstrap procedure" can be used to extrapolate from a linear model of a rank-2 tensor to a full non-linear theory of gravity (i.e., general relativity) via a coupling to the stress-energy of the model. In this work, I extend this procedure to a "Lorentz-violating" gravitational model, in which the linear tensor field and the matter fields "see" different metrics due to a coupling between the tensor field and a background vector field. The resulting model can be thought of as a generalized Proca theory with a non-minimal coupling to conventional matter. It has a similar linearized limit to the better-known "bumblebee model", but differs at higher orders in perturbation theory. Its effects are unobservable in FRW spacetimes, but are expected to be important in anisotropic cosmological spacetimes.