Noether symmetries and boundary terms in extended Teleparallel gravity cosmology

TL;DR

This paper uses Noether symmetries to identify exact solutions in extended Teleparallel gravity models involving torsion and boundary terms within flat FRW cosmology.

Contribution

It introduces a method to select functional forms and solutions in extended Teleparallel gravity using Noether symmetries, focusing on scalar invariants and boundary terms.

Findings

Derived several physically consistent models.

Obtained exact solutions for the cosmological dynamics.

Identified functional forms via symmetry approach.

Abstract

We discuss an extended Teleparallel gravity models comprising functions of scalar invariants constructed by torsion, torsion Gauss-Bonnet and boundary terms. We adopt the Noether Symmetry Approach to select the functional forms, the first integrals and, eventually, the exact solutions of the dynamics in the context of flat Friedman-Robertson-Walker cosmology. Standard perfect fluid matter, minimally coupled to geometry, is considered. Several physically consistent models are derived with related exact solutions.