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Kantowski-Sachs and Bianchi III dynamics in $f\left(Q\right)$-gravity

Alfredo D. Millano, K. Dialektopoulos, N. Dimakis, A. Giacomini, H. Shababi, Amlan Halder, A. Paliathanasis

Abstract

We explore the phase-space of homogeneous and anisotropic spacetimes within symmetric teleparallel $f(Q)$-gravity. Specifically, we consider the Kantowski-Sachs and locally rotational Bianchi III geometries to describe the physical space. By analyzing the phase-space, we reconstruct the cosmological history dictated by $f(Q)$-gravity and comment about the theory's viability. Our findings suggest that the free parameters of the connection must be constrained to eliminate nonlinear terms in the field equations. Consequently, new stationary points emerge, rendering the theory cosmologically viable. We identify the existence of anisotropic accelerated universes, which may correspond to the pre-inflationary epoch.

Kantowski-Sachs and Bianchi III dynamics in $f\left(Q\right)$-gravity

Abstract

We explore the phase-space of homogeneous and anisotropic spacetimes within symmetric teleparallel -gravity. Specifically, we consider the Kantowski-Sachs and locally rotational Bianchi III geometries to describe the physical space. By analyzing the phase-space, we reconstruct the cosmological history dictated by -gravity and comment about the theory's viability. Our findings suggest that the free parameters of the connection must be constrained to eliminate nonlinear terms in the field equations. Consequently, new stationary points emerge, rendering the theory cosmologically viable. We identify the existence of anisotropic accelerated universes, which may correspond to the pre-inflationary epoch.
Paper Structure (9 sections, 36 equations, 1 figure)

This paper contains 9 sections, 36 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Symmetric Teleparallel Geometry and gravity
  3. Symmetric Teleparallel Equivalent of General Relativity
  4. $f(Q)$-Theory
  5. Flat FLRW Cosmology in $f(Q)$ gravity
  6. Kantowski-Sachs and Bianchi III geometry
  7. Phase-space analysis
  8. General case
  9. Concluding remarks

Figures (1)

  • Figure 2: Evolution of $\Omega_{R}, y, \Sigma, x, Z$ evaluated at a numerical solutions of system \ref{['ds-1-special']}-\ref{['ds-4-special']} for $\alpha=\pm \frac{1}{2}$ and $\lambda=1$ for initial conditions (i.c.) near the points $P_{2}$ and $P_{3}$ with a displacement of $\epsilon=\frac{1}{1000}.$ Also present as a red dotted line is the evolution of the deceleration parameter $q$ evaluated at these points.