Self-tuning vacuum variable and cosmological constant

A spacetime-independent variable is introduced which characterizes a Lorentz-invariant self-sustained quantum vacuum. For a perfect (Lorentz-invariant) quantum vacuum, the self-tuning of this variable nullifies the effective energy density which enters the low-energy gravitational field equations. The observed small but nonzero value of the cosmological constant may then be explained as corresponding to the effective energy density of an imperfect quantum vacuum (perturbed by, e.g., the presence of thermal matter).Comment: 28 pages with revtex4; v6: preprint version of published paper with detailed reference

Strongly-resonant p-wave superfluids

We study theoretically a dilute gas of identical fermions interacting via a p-wave resonance. We show that, depending on the microscopic physics, there are two distinct regimes of p-wave resonant superfluids, which we term "weak" and "strong". Although expected naively to form a BCS-BEC superfluid, a strongly-resonant p-wave superfluid is in fact unstable towards the formation of a gas of fermionic triplets. We examine this instability and estimate the lifetime of the p-wave molecules due to the collisional relaxation into triplets. We discuss consequences for the experimental achievement of p-wave superfluids in both weakly- and strongly-resonant regimes

Big bang as a topological quantum phase transition

It has been argued that a particular type of quantum-vacuum variable q can provide a solution to the main cosmological constant problem and possibly also give a cold-dark-matter component. We now show that the same q field may suggest a new interpretation of the big bang, namely as a quantum phase transition between topologically inequivalent vacua. These two vacua are characterized by the equilibrium values q=±q0, and there is a kink-type solution q(t) interpolating between q=−q0 for t→−∞ and q=+q0 for t→∞, with conformal symmetry for q=0 at t=0

Quantum phase transition for the BEC--BCS crossover in condensed matter physics and CPT violation in elementary particle physics

We discuss the quantum phase transition that separates a vacuum state with fully-gapped fermion spectrum from a vacuum state with topologically-protected Fermi points (gap nodes). In the context of condensed-matter physics, such a quantum phase transition with Fermi point splitting may occur for a system of ultracold fermionic atoms in the region of the BEC-BCS crossover, provided Cooper pairing occurs in the non-s-wave channel. For elementary particle physics, the splitting of Fermi points may lead to CPT violation, neutrino oscillations, and other phenomena.Comment: 13 pages, 1 figure, v3: published versio

Osmotic pressure of matter and vacuum energy

The walls of the box which contains matter represent a membrane that allows the relativistic quantum vacuum to pass but not matter. That is why the pressure of matter in the box may be considered as the analog of the osmotic pressure. However, we demonstrate that the osmotic pressure of matter is modified due to interaction of matter with vacuum. This interaction induces the nonzero negative vacuum pressure inside the box, as a result the measured osmotic pressure becomes smaller than the matter pressure. As distinct from the Casimir effect, this induced vacuum pressure is the bulk effect and does not depend on the size of the box. This effect dominates in the thermodynamic limit of the infinite volume of the box. Analog of this effect has been observed in the dilute solution of 3He in liquid 4He, where the superfluid 4He plays the role of the non-relativistic quantum vacuum, and 3He atoms play the role of matter.Comment: 5 pages, 1 figure, JETP Lett. style, version accepted in JETP Letter

ℏ\hbar as parameter of Minkowski metric in effective theory

With the proper choice of the dimensionality of the metric components, the action for all fields becomes dimensionless. Such quantities as the vacuum speed of light c, the Planck constant \hbar, the electric charge e, the particle mass m, the Newton constant G never enter equations written in the covariant form, i.e., via the metric g^{\mu\nu}. The speed of light c and the Planck constant are parameters of a particular two-parametric family of solutions of general relativity equations describing the flat isotropic Minkowski vacuum in effective theory emerging at low energy: g^{\mu\nu}=diag(-\hbar^2, (\hbar c)^2, (\hbar c)^2, (\hbar c)^2). They parametrize the equilibrium quantum vacuum state. The physical quantities which enter the covariant equations are dimensionless quantities and dimensionful quantities of dimension of rest energy M or its power. Dimensionless quantities include the running coupling `constants' \alpha_i; topological and geometric quantum numbers (angular momentum quantum number j, weak charge, electric charge q, hypercharge, baryonic and leptonic charges, number of atoms N, etc). Dimensionful parameters include the rest energies of particles M_n (or/and mass matrices); the gravitational coupling K with dimension of M^2; cosmological constant with dimension M^4; etc. In effective theory, the interval s has the dimension of 1/M; it characterizes the dynamics of particles in the quantum vacuum rather than geometry of space-time. We discuss the effective action, and the measured physical quantities resulting from the action, including parameters which enter the Josepson effect, quantum Hall effect, etc.Comment: 18 pages, no figures, extended version of the paper accepted in JETP Letter

Vacuum energy: quantum hydrodynamics vs quantum gravity

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 Letter