Modelling Planck-scale Lorentz violation via analogue models

TL;DR

This paper explores how analogue models using two-component Bose-Einstein condensates can simulate Planck-scale Lorentz violations, providing insights into the naturalness problem in quantum gravity phenomenology.

Contribution

It introduces a condensed-matter analogue model that demonstrates high-energy Lorentz violations without the naturalness problem occurring.

Findings

The model exhibits Lorentz invariance violation due to ultraviolet physics.

It provides an explicit example where the naturalness problem is avoided.

The approach offers a new perspective on quantum gravity phenomenology.

Abstract

Astrophysical tests of Planck-suppressed Lorentz violations had been extensively studied in recent years and very stringent constraints have been obtained within the framework of effective field theory. There are however still some unresolved theoretical issues, in particular regarding the so called "naturalness problem" - which arises when postulating that Planck-suppressed Lorentz violations arise only from operators with mass dimension greater than four in the Lagrangian. In the work presented here we shall try to address this problem by looking at a condensed-matter analogue of the Lorentz violations considered in quantum gravity phenomenology. Specifically, we investigate the class of two-component BECs subject to laser-induced transitions between the two components, and we show that this model is an example for Lorentz invariance violation due to ultraviolet physics. We shall show that such a model can be considered to be an explicit example high-energy Lorentz violations where the ``naturalness problem'' does not arise.