  The cosmological constant is one of the most pressing problems in modern
physics. We address this issue from an emergent gravity standpoint, by using an
analogue gravity model. Indeed, the dynamics of the emergent metric in a
Bose-Einstein condensate can be described by a Poisson-like equation with a
vacuum source term reminiscent of a cosmological constant. The direct
computation of this term shows that in emergent gravity scenarios this constant
may be naturally much smaller than the naive ground-state energy of the
emergent effective field theory. This suggests that a proper computation of the
cosmological constant would require a detailed understanding about how Einstein
equations emerge from the full microscopic quantum theory. In this light, the
cosmological constant appears as a decisive test bench for any quantum or
emergent gravity scenario.
