Effective gravity and quantum vacuum in superfluids

Quantum liquids, in which an effective Lorentzian metric (and thus some kind of gravity) gradually arise in the low-energy corner, are systems 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 is the observed vacuum energy at least 120 orders of magnitude smaller than the naive estimate derived 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 perturbation of quantum vacuum caused by matter (quasiparticles), curvature, and other possible sources, naturally leading to a smooth component — the quintessence. This provides the possible solution of another cosmological constant problem: Why is the present cosmological constant 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.