  Quantum liquids, in which an effective Lorentzian metric and thus some kind
of gravity gradually arise in the low-energy corner, are the objects where the
problems related to the quantum vacuum can be investigated in detail. In
particular, they provide the possible solution of the cosmological constant
problem: why the vacuum energy is by 120 orders of magnitude smaller than the
estimation from the relativistic quantum field theory. The almost complete
cancellation of the cosmological constant does not require any fine tuning and
comes from the fundamental ``trans-Planckian'' physics of quantum liquids. The
remaining vacuum energy is generated by the perturbations of quantum vacuum
caused by matter (quasiparticles), curvature, and other possible sources, such
as smooth component -- the quintessence. This provides the possible solution of
another cosmological constant problem: why the present cosmological constant is
on the order of the present matter density of the Universe. We discuss here
some properties of the quantum vacuum in quantum liquids: the vacuum energy
under different conditions; excitations above the vacuum state and the
effective acoustic metric for them provided by the motion of the vacuum;
Casimir effect, etc.
