Noether Symmetry Approach in $f(T,B)$ teleparallel cosmology

TL;DR

This paper explores $f(T,B)$ gravity in cosmology, demonstrating how it encompasses various gravity theories and using Noether symmetry to find cosmological solutions.

Contribution

It introduces the $f(T,B)$ gravity framework and applies Noether symmetry to derive solutions, unifying different gravity models.

Findings

Unified $f(T,B)$ framework includes $f(T)$, $f(R)$, and $f(R,T)$ gravities.

Noether symmetry approach yields specific cosmological solutions.

Demonstrates the versatility of $f(T,B)$ in cosmological modeling.

Abstract

We consider the cosmology derived from $f(T,B)$ gravity where $T$ is the torsion scalar and $B=\frac{2}{e}\partial_{\mu}(e T^{\mu})$ a boundary term. In particular we discuss how it is possible to recover, under the same standard, the teleparallel $f(T)$ gravity, the curvature $f(R)$ gravity and the teleparallel-curvature $f(R,T)$ gravity, which are particular cases of $f(T,B)$. We adopt the Noether Symmetry Approach to study the related dynamical systems and to find out cosmological solutions.