Dynamical complexity of the Teleparallel gravity cosmology

TL;DR

This paper extends the dynamical systems analysis of teleparallel gravity cosmology by introducing a nonconstant degree of freedom, enabling better modeling of the Hubble constant and addressing the $H_0$ tension.

Contribution

It generalizes previous autonomous systems in teleparallel gravity by allowing a variable degree of freedom, facilitating a more flexible analysis of cosmological evolution and the $H_0$ tension.

Findings

Identifies hyperbolic critical points in the generalized dynamical system.

Demonstrates the potential to fit the $H_0$ value within a viable $f(T,B)$ model.

Provides a scenario to address the $H_0$ tension at late times.

Abstract

The exploration of teleparallel gravity has been done from a dynamical systems point of view in order to be tested against the cosmological evolution currently observed. So far, the proposed autonomous systems have been restrictive over a constant dynamical variable, which contains information related to the dynamics on the $H_0$ value. It is therefore that in this paper we consider a generalization of the dynamical system by imposing a nonconstant degree of freedom over it which allows us to rewrite a generic autonomous dynamical analysis. We describe the treatment of our nonlinear autonomous system by studying the hyperbolic critical points and discuss an interesting phenomenological feature in regards to $H_0$: the possibility to obtain a best-fit value for this parameter in a cosmologically viable $f(T,B)$ model, a mixed power law. This result allows us to present a generic scenario in which it is possible to fix constraints to solve the $H_0$ tension at late times where its linearized solutions are considered.