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Vacuum energy and cosmological constant: View from condensed matter

G. E. Volovik
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Abstract

The condensed matter examples, in which the effective gravity appears in the low-energy corner as one of the collective modes of quantum vacuum, provide a possible answer to the question, why the vacuum energy is so small. This answer comes from the fundamental ``trans-Planckian'' physics of quantum liquids. In the effective theory of the low energy degrees of freedom the vacuum energy density is proportional to the fourth power of the corresponding ``Planck'' energy appropriate for this effective theory. However, from the exact ``Theory of Everything'' of the quantum liquid it follows that its vacuum energy density is exactly zero without fine tuning, if: there are no external forces acting on the liquid; there are no quasiparticles which serve as matter; no space-time curvature; and no boundaries which give rise to the Casimir effect. Each of these four factors perturbs the vacuum state and induces the nonzero value of the vacuum energy density of order of energy density of the perturbation. This is the reason, why one must expect that in each epoch the vacuum energy density is of order of matter density of the Universe, or/and of its curvature, or/and of the energy density of smooth component -- the quintessence.

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G. E. Volovik. 2001-04-02. Vacuum energy and cosmological constant: View from condensed matter. https://arxiv.org/abs/gr-qc/0101111

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