Quantum potential induced emergence of massive scalar fields in the analogue gravity model of a Bose-Einstein condensate

We show here a general approach to include the quantum potential term in the emergent gravity model of Bose-Einstein condensate by using multiple scales. Our main result shows the emergence of a massive scalar modulating field at larger length scales as a result of Lorentz symmetry breaking at the length scales comparable to the healing length. We also propose that, the nonlocal interactions induced tuning of healing length can be exploited experimentally to observe the systematics of small and large scale coupling as emerges in our present analysis.