  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.

General Relativity and Quantum Cosmology;Other Condensed Matter