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Nonlinear spinor field with Lyras geometry: Bianchi type-VI space-time

Bijan Saha

Abstract

In the context of a Bianchi type-VI space-time characterized by Lyras geometry, we investigate the influence of a nonlinear spinor field on the evolution of the Universe. Our previous research has examined the nonlinear spinor field within Bianchi diagonal models, revealing that the spinor field exhibits non-trivial non-diagonal components of the energy-momentum tensor. These components impose various constraints on both the space-time geometry and the spinor field itself. The incorporation of Lyras geometry into the framework does not alleviate these constraints; however, it alters the preservation of the energy-momentum tensor. Furthermore, this integration complicates the relationship between the invariants of the spinor field and the space-time, ultimately affecting the outcomes of our analysis. Moreover, in this case energy-momentum tensor does not preserve.

Nonlinear spinor field with Lyras geometry: Bianchi type-VI space-time

Abstract

In the context of a Bianchi type-VI space-time characterized by Lyras geometry, we investigate the influence of a nonlinear spinor field on the evolution of the Universe. Our previous research has examined the nonlinear spinor field within Bianchi diagonal models, revealing that the spinor field exhibits non-trivial non-diagonal components of the energy-momentum tensor. These components impose various constraints on both the space-time geometry and the spinor field itself. The incorporation of Lyras geometry into the framework does not alleviate these constraints; however, it alters the preservation of the energy-momentum tensor. Furthermore, this integration complicates the relationship between the invariants of the spinor field and the space-time, ultimately affecting the outcomes of our analysis. Moreover, in this case energy-momentum tensor does not preserve.
Paper Structure (9 sections, 52 equations, 3 figures)

This paper contains 9 sections, 52 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Basic equations
  3. Weyl's geometry:
  4. Lyra's geometry:
  5. Spinor field
  6. Bianchi type-VI model
  7. Einstein equation
  8. Numerical solutions
  9. Concluding remarks

Figures (3)

  • Figure 1: Evolution of metric functions $a_1(t)$ (blue long dash), $a_2(t)$ (red dash-dot) and $a_3(t)$ (black solid) with Lyra geometry when spinor field nonlinearity simulates modified Chaplygin gas.
  • Figure 2: Evolution of directional Hubble parameters $H_1(t)$ (blue long dash), $H_2(t)$ (red dash-dot) and $H_3(t)$ (black solid) with Lyra geometry when spinor field nonlinearity simulates modified Chaplygin gas.
  • Figure 3: Evolution of Lyra parameter $\beta(t)$ when spinor field nonlinearity simulates modified Chaplygin gas.