Spin 1/2 Particles in Oscillating de Sitter Universe: Reflection from the Cosmological Barrier

Abstract

It is known that geometry of the Lobachevsky space acts on particles with spins 0, 1/2, 1 as an ideal mirror distributed in space. The depth of penetration of the field in such an effective medium increases with increasing the field energy, also this penetration depends on the radius of curvature of the Lobachevsky space. 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 effectively lead to redistribution of the particle density in space. The earlier analysis assumed the static nature of the space-time geometry. In this paper we generalize the investigation for the spin 1/2 field in the case of oscillating de Sitter universe. The Dirac equation is solved in non-static quasiCartesian coordinates. At this we substantially use a generalized helicity operator. The wave functions of the particle depend nontrivially on the time, however the effect of the complete reflection of the particles from the effective potential barrier is preserved. For real Majorana 4-spinor field similar results are valid as well.