Vacuum energy: quantum hydrodynamics vs quantum gravity

G. E. Volovik

Low Temperature Laboratory, Helsinki University of Technology, FIN-02015 HUT, Finland

L. D. Landau Institute for Theoretical Physics, 117334 Moscow, Russia

PACS: 03.70.+k, 04.90.+e, 67.90.+z, 98.80.Es

**Abstract**

We compare quantum hydrodynamics and quantum gravity. They
share many common features. In particular, both have quadratic
divergences, and both lead to the problem of the vacuum energy,
which in the quantum gravity transforms to the cosmological
constant problem. We show that in quantum liquids the vacuum
energy density is not determined by the quantum
zero-point energy of the phonon modes. The energy density
of the vacuum is much smaller and is determined by the
classical macroscopic parameters of the liquid including the
radius of the liquid droplet. In the same manner the
cosmological constant is not determined by the
zero-point energy of quantum fields. It is much
smaller and is determined by the classical macroscopic
parameters of the Universe dynamics: the Hubble radius, the
Newton constant and the energy density of matter.
The same may
hold for the Higgs mass problem: the
quadratically divergent
quantum correction to the Higgs potential mass term is also
cancelled by the microscopic (trans-Planckian) degrees of
freedom due to thermodynamic stability of the
whole quantum vacuum.