Lorentz Invariance Violation in Modified Gravity

TL;DR

This paper explores how modified gravity models with environment-dependent Lorentz invariance violation could cause superluminal fermions, with potential observational tests via neutrino speed measurements and lunar ranging, especially in chameleon models.

Contribution

It introduces a framework for Lorentz invariance violation in scalar-tensor modified gravity models and analyzes their phenomenological constraints and observational signatures.

Findings

Fermions can have superluminal speeds along scalar field lines.

Chameleon models satisfy observational constraints from Cerenkov radiation.

Neutrino speed measurements can probe scalar field profiles in dense environments.

Abstract

We consider an environmentally dependent violation of Lorentz invariance in scalar-tensor models of modified gravity where General Relativity is retrieved locally thanks to a screening mechanism. We find that fermions have a modified dispersion relation and would go faster than light in an anisotropic and space-dependent way along the scalar field lines of force. Phenomenologically, these models are tightly restricted by the amount of Cerenkov radiation emitted by the superluminal particles, a constraint which is only satisfied by chameleons. Measuring the speed of neutrinos emitted radially from the surface of the earth and observed on the other side of the earth would probe the scalar field profile of modified gravity models in dense environments. We argue that the test of the equivalence principle provided by the Lunar ranging experiment implies that a deviation from the speed of light, for natural values of the coupling scale between the scalar field and fermions, would be below detectable levels, unless gravity is modified by camouflaged chameleons where the field normalisation is environmentally dependent.