Noether Symmetry in f(T) Theory at the anisotropic universe

TL;DR

This paper investigates Noether symmetry in f(T) gravity within an anisotropic Bianchi type I universe, deriving exact solutions and identifying conditions for positive cosmic expansion.

Contribution

It introduces a formalism for applying Noether symmetry to f(T) gravity in anisotropic settings and finds specific power-law solutions consistent with symmetry requirements.

Findings

Power-law f(T) models satisfy Noether symmetry in anisotropic universe.

Explicit exact solutions are derived under symmetry constraints.

Conditions for positive expansion are established.

Abstract

As it is well known, symmetry plays a crucial role in the theoretical physics. On other hand, the Noether symmetry is a useful procedure to select models motivated at a fundamental level, and to discover the exact solution to the given lagrangian. In this work, Noether symmetry in f(T) theory on a spatially homogeneous and anisotropic Bianchi type I universe is considered. We discuss the Lagrangian formalism of f(T) theory in anisotropic universe. The point-like Lagrangian is clearly constructed.The explicit form of f(T) theory and the corresponding exact solution are found by requirement of Noether symmetry and Noether charge. A power-law f(T), the same as the FRW universe, can satisfy the required Noether symmetry in the anisotropic universe with power- law scale factor. It is regarded that positive expansion is satisfied by a constrain between parameters.