Abstract
Based upon the exact formal solutions of the Weyl–Dirac-equation in anisotropic planar Bianchi-type-I background spacetimes with power law scale factors, one can introduce suitable equivalence classes of the solutions of these models. The associated background spacetimes are characterized by two parameters. It is shown that the exact solutions of all models of a given equivalence class can be generated with the help of a special transformation of these two parameters, provided one knows a single exact solution of an arbitrary member of this class. The method can also be utilized to derive approximate solutions, i.e. solutions which exhibit the correct behavior at early and at late times as well. This is explicitly demonstrated for the case of the anisotropic Kasner background with axial symmetry.
Highlights
The study of particles, which obey Dirac’s equation and propagate in curved spacetime backgrounds, has occupied physicists for quite some time because of their importance in cosmological problems
Based upon the exact formal solutions of the Weyl–Dirac-equation in anisotropic planar Bianchi-type-I background spacetimes with power law scale factors, one can introduce suitable equivalence classes of the solutions of these models
It is shown that the exact solutions of all models of a given equivalence class can be generated with the help of a special transformation of these two parameters, provided one knows a single exact solution of an arbitrary member of this class
Summary
The study of particles, which obey Dirac’s equation and propagate in curved spacetime backgrounds, has occupied physicists for quite some time because of their importance in cosmological problems. To establish an isotropic FLRW background during cosmic inflation, one introduces, instead of considering only a single vector field, either three mutually orthogonal vector fields with the additional constraint that these fields must have exactly the same magnitude (“cosmic triad”) [10,11], or alternatively a large number of randomly oriented vector fields [11] In the latter case a small amount of a few percent of global anisotropy survives the inflation-. Barut and Duru investigated massless and massive fermions in two flat FLRW spacetimes with power-law expansion, and in the steady-state part of de Sitter spacetime [14]. The latter model had been studied by Cotaescu, who in addition performed the quantization of the spin-.
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