A study on the Friedmann like Universe with Torsion using Noether Symmetry

TL;DR

This paper applies Noether symmetry analysis to Einstein-Cartan theory with torsion in FRW cosmology, revealing that torsion induces a de Sitter phase in the universe's evolution.

Contribution

It introduces a novel application of Noether symmetry to Einstein-Cartan theory, deriving solutions that show torsion leads to a de Sitter universe.

Findings

Torsion causes the universe to be in a de Sitter phase.

Noether symmetry helps find conserved quantities and solutions in torsion-inclusive cosmology.

The approach links symmetry analysis with cosmological dynamics in Einstein-Cartan theory.

Abstract

This paper deals with the symmetry analysis of the Einstein Cartan theory which is an extension of the General Relativity and it accounts for the space-time torsion. We begin by applying Noether Theorem to the Lagrangian of the FRW type cosmology with torsion and choose a point transformation: $(a,\phi,N)\rightarrow(u,v,W)$, such that one of the transformed variable is cyclic for the Lagrangian. Then using the conserved charge, which is obtained by applying Noether theorem, and the constant of motion, we get the solutions and conclude that due to the presence of torsion the FRW type cosmology is in the de Sitter phase.