Cosmological dynamics of dark energy in scalar-torsion $f(T,\phi)$ gravity

TL;DR

This paper explores the cosmological behavior of scalar-torsion $f(T,)$ gravity, revealing new attractors with accelerated expansion and scaling solutions that describe different cosmic epochs, including the current dark energy dominance.

Contribution

It introduces a detailed analysis of the stability and cosmological implications of non-linear $f(T,)$ models with exponential potential, identifying novel attractors and scaling solutions.

Findings

Discovery of new accelerated attractors.

Identification of scaling solutions for dark energy and background fluids.

System transitions from scaling epochs to dark energy domination.

Abstract

It is investigated the cosmological dynamics of scalar-torsion $f(T,\phi)$ gravity as a dark energy model, where $T$ is the torsion scalar of teleparallel gravity and $\phi$ is a canonical scalar field. In this context, we are concerned with the phenomenology of the class of models with non-linear coupling to gravity and exponential potential. We obtain the critical points of the autonomous system, along with the stability conditions of each one of them and their cosmological properties. Particularly, we show the existence of new attractors with accelerated expansion, as well as, new scaling solutions in which the energy density of dark energy scales as the background fluid density, thus, defining the so-called scaling radiation and scaling matter epochs. The scaling solutions are saddle points, and therefore, the system exits these solutions to the current epoch of cosmic acceleration, towards an attractor point describing the dark energy-dominated era.