Classical and quantum cosmological solutions in teleparallel dark energy with anisotropic background geometry

TL;DR

This paper derives exact classical and quantum solutions in teleparallel dark energy models with anisotropic geometries, using variational symmetries to find invariant functions and conservation laws.

Contribution

It introduces a method to obtain analytic solutions in anisotropic teleparallel cosmologies through symmetry analysis, including quantum wavefunctions.

Findings

New classical solutions for Bianchi I, Bianchi III, and Kantowski-Sachs geometries.

Exact quantum wavefunctions derived for the cosmological models.

Demonstrates the utility of variational symmetries in solving complex cosmological equations.

Abstract

We investigate exact and analytic solutions for the field equations in teleparallel dark energy model where the physical space is described by the locally rotational symmetric Bianchi I, Bianchi III and Kantowski-Sachs geometries. We make use of the property that a point-like Lagrangian exist for the description of the field equations and variational symmetries are applied for the construction of invariant functions and conservation laws. The later are used for the derivation of new analytic solutions for the classical field equations and exact function forms for the wavefunction in the quantum limit.