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Authors: G. E. Volovik Title: Vacuum energy: quantum hydrodynamics vs quantum gravity Subject: General Relativity and Quantum Cosmology, Condensed Matter - Soft Condensed Matter, High Energy Physics - Phenomenology
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.
Comment: 14 pages, no figures, added section on the problem of Higgs mass,
version accepted for the special issue of JETP Letters
