Expansion-contraction duality breaking in a Planck-scale sensitive cosmological quantum simulator

We propose the experimental simulation of cosmological perturbations governed by a Planck-scale induced Lorentz violating dispersion, aimed at distinguishing between early-universe models with similar power spectra. Employing a novel variant of the scaling approach for the evolution of a Bose-Einstein condensate with both contact and dipolar interactions, we capture the hitherto unobserved phenomenon of trans-Planckian damping. We show that scale invariance, and in turn, the duality of the power spectrum is subsequently broken at large momenta for an inflating gas, and at small momenta for a contracting gas. We thereby furnish a Planck-scale sensitive approach to analogue quantum cosmology that can readily be implemented in the quantum gas laboratory.