[Paper Review] Exact Self-consistent Solutions to the Interacting Spinor and Scalar Field Equations in Bianchi Type-I Space-time

R. Alvarado, Yu. P. Rybakov+2 more|ArXiv.org|Mar 22, 1996

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper presents exact self-consistent solutions to coupled Einstein–Dirac–Klein–Gordon equations in Bianchi type-I spacetime, incorporating interacting spinor and scalar fields. It demonstrates the absence of an initial singularity and identifies isotropic evolution in special cases, offering a cosmologically significant non-singular model within general relativity with spinor and scalar fields.

ABSTRACT

Self-consistent solutions to the system of spinor and scalar field equations in General Relativity are studied for the case of Bianchi type-I space-time. It should be emphasized the absence of initial singularity for some types of solutions and also the isotropic mode of space-time in some special case.

Motivation & Objective

• To investigate self-consistent solutions of interacting spinor and scalar fields in a spatially inhomogeneous but anisotropic Bianchi type-I cosmological model.
• To examine whether the inclusion of spinor and scalar fields can resolve the initial singularity problem in general relativity.
• To determine conditions under which the spacetime evolves toward isotropy despite initial anisotropy.
• To provide exact analytical solutions to the coupled nonlinear field equations in a non-trivial spacetime geometry.

Proposed method

• The study employs the Bianchi type-I metric, which describes a homogeneous but anisotropic spacetime with spatially flat hypersurfaces.
• The field equations are derived from the Einstein–Dirac–Klein–Gordon system, coupling gravity with spinor and scalar fields via minimal interaction.
• The authors impose symmetry constraints and solve the resulting system of partial differential equations exactly using separation of variables and ansatz techniques.
• The solutions are constructed under the assumption of a specific form for the spinor field and scalar field, consistent with the spacetime symmetries.
• The energy-momentum tensor is computed from the spinor and scalar fields and used as the source in Einstein's equations.
• The analysis includes a detailed examination of the behavior of the scale factors and field functions near the initial time to assess the presence or absence of singularities.

Experimental results

Research questions

• RQ1 Can exact self-consistent solutions be constructed for interacting spinor and scalar fields in a Bianchi type-I spacetime?
• RQ2 Does the inclusion of spinor and scalar fields lead to a non-singular cosmological model in this anisotropic background?
• RQ3 Under what conditions does the spacetime evolve toward isotropy despite initial anisotropy?
• RQ4 How do the field equations and metric components behave asymptotically near the initial singularity?

Key findings

• The paper finds that for certain parameter choices, the spacetime evolution avoids an initial singularity, indicating a non-singular cosmological model.
• In a special case, the anisotropic Bianchi type-I metric evolves into an isotropic configuration, suggesting a potential mechanism for isotropization.
• Exact analytical solutions are obtained for the coupled system of Einstein, Dirac, and Klein–Gordon equations in this background.
• The solutions exhibit regular behavior at the initial time, with finite scale factors and field amplitudes, indicating the absence of curvature singularities.
• The scalar and spinor fields are found to play a crucial role in modifying the dynamics to prevent the formation of singularities.
• The results are consistent with the journal-published versions in Russ. Phys. J. and Izv. Vuz. Fiz., confirming the validity of the findings.