Naturalness in an emergent analogue spacetime

Effective field theories (EFTs) have been widely used as a framework in order to place constraints on the Planck suppressed Lorentz violations predicted by various models of quantum gravity. There are, however, technical problems in the EFT framework when it comes to ensuring that small Lorentz violations remain small-this is the essence of the "naturalness" problem. Herein we present an "emergent" spacetime model, based on the "analogue gravity" program, by investigating a specific condensed-matter system. Specifically, we consider the class of two-component BECs subject to laser-induced transitions between the components, and we show that this model is an example for Lorentz invariance violation due to ultraviolet physics. Furthermore, our model explicitly avoids the naturalness problem, and makes specific suggestions regarding how to construct a physically reasonable quantum gravity phenomenology.