Dirac, Majorana and Weyl particles in the oscillating de Sitter universe, reflection from the cosmological barrier

Abstract

It is known that the geometry of the Lobachevsky space acts on the fields of particles with spins 0, 1/2, 1 as an ideal mirror distributed in space. The depth of penetration of the field in such a medium increases with increasing field energy. Since the Lobachevsky model is a constituent element in some cosmological models, this property means that in such models it is necessary to take into account the effect of the presence of a “cosmological mirror”; it must lead to a redistribution of the particle density in space. The earlier analysis assumed the static nature of the space-time geometry. In this article, we generalize the research of the spin 1/2 field in the case of the oscillating model of the de Sitter universe. The Dirac equation is solved in the non-static quasi-Cartesian coordinates. At this, we substantially use the diagonalization of a generalized helicity operator. The wave functions of the particle are nontrivially time-dependent; however the effect of a complete reflection of the particles from an effective potential barrier is preserved. For the real Majorana 4-spinor field, the similar results are valid. For the solutions describing the reflection effect to be constructed, we must use linear combinations of solutions with opposite helicities. Such combinations are forbidden for 2-component Weyl particles, for this reason such particles cannot be reflected by the cosmological barrier.