G. Volovik
We continued to study the least known features of high-energy physics and cosmology - the properties of the quantum vacuum - using the condensed matter analogy.
In collaboration with A.I. Zelnikov from University of Alberta (Canada) we studied temperature correction to the free energy of the gravitational field. We found that the leading correction to the Newton constant is universal since it is determined only by the number of fermionic and bosonic fields, and does not depend on whether or not the gravitational field obeys the Einstein equations. Exactly the same corrections exist in the hydrodynamic of quantum liquids, such as superfluid 3He and 4He, where they can be measured.
In relation to the problem of cosmological constant and vacuum energy, which was usually thought of as the subject of general relativity, we found that the vacuum energy is important for the Universe even in the absence of gravity. We calculated the vacuum energy in the presence of matter in special relativity, and found that, as in general relativity, the vacuum energy density is on the order of the energy density of matter.
In general relativity we considered the vacuum response to the non-steady-state perturbations. The phenomenological theory was suggested for the time dependent cosmological constant, in which the Einstein equations are slightly modified to include the non-covariant corrections.
We suggested modification of the Pati-Salam model of the unification of quarks and leptons adding the SU(4) family group for four generations of fermions. In this model the creation of baryons and leptons in the process of electroweak baryogenesis must be accompanied by the creation of fermions of the 4-th generation. As a result the excess of baryons over antibaryons leads to the excess of neutrinos over antineutrinos in the 4-th generation. This fourth-generation neutrino is about 50 times heavier than baryion, and thus it may be a good candidate for the non-baryonic dark matter.