Dynamics in interacting scalar-torsion theory

TL;DR

This paper investigates a scalar-torsion gravitational model with dark sector interactions, revealing stable solutions like inflationary and de Sitter universes, and analyzing their implications for cosmological evolution.

Contribution

It introduces a novel scalar-torsion model with dark sector coupling, analyzing its dynamical behavior and identifying stable cosmological solutions relevant to the universe's evolution.

Findings

Existence of inflationary scaling solutions

Recovery of de Sitter universe

Identification of a stable attractor solution

Abstract

In a spatially flat \ Friedmann--Lema\^{\i}tre--Robertson--Walker background space we consider a scalar-torsion gravitational model which has similar properties with the dilaton theory. This teleparallel model is invariant under a discrete transformation similar to the Gasperini-Veneziano duality transformation. Moreover, in the gravitational Action integral we introduce the Lagrangian function of a pressureless fluid source which is coupled to the teleparallel dilaton field. This specific gravitational theory with interaction in the dark sector of the universe is investigated by using methods of the dynamical system analysis. We calculate that the theory provides various areas of special interest for the evolution of the cosmological history. Inflationary scaling solutions and the de Sitter universe is recovered. Furthermore, we calculate that there exist an attractor which provides a stable solution where the two fluid components, the scalar field and the pressureless matter, contribute in the cosmological fluid. This solution is of special interest because it can describe the present epoch. Finally, the qualitative evolution of the cosmographic parameters is discussed.