Analogue quantum gravity phenomenology from a two-component Bose-Einstein condensate

We present an analogue-emergent spacetime that reproduces the salient features of the most common ansatze used for quantum gravity phenomenology. We do this by investigating a system of two-coupled Bose-Einstein condensates. This system can be tuned to have two 'phonon' modes (one massive, one massless) which share the same limiting speed in the hydrodynamic approximation. The system nevertheless possesses (possibly non-universal) Lorentz violating terms once 'quantum pressure' becomes important. We investigate the physical interpretation of the relevant fine-tuning conditions, and discuss the possible lessons and hints that this analogue spacetime could provide for the phenomenology of real physical quantum gravity. In particular we show that the effective field theory of quasi-particles in such an emergent spacetime does not exhibit the so-called 'naturalness problem'.