# Dynamical system analysis of dark energy models in scalar coupled metric-torsion theories

## TL;DR

This paper analyzes the phase space dynamics of dark energy models within scalar coupled metric-torsion theories, identifying stable solutions that can explain cosmic acceleration without direct interaction with matter.

## Contribution

It introduces a detailed phase space analysis of non-minimal scalar-torsion couplings, identifying conditions for stable, accelerating solutions in both Einstein and Jordan frames.

## Key findings

- Stable critical points correspond to accelerated expansion.
- Evolution profiles match earlier exact solutions.
- Physical viability depends on coupling parameter regions.

## Abstract

We study the phase space dynamics of cosmological models in the theoretical formulations of non-minimal metric-torsion couplings with a scalar field, and investigate in particular the critical points which yield stable solutions exhibiting cosmic acceleration driven by the {\em dark energy}. The latter is defined in a way that it effectively has no direct interaction with the cosmological fluid, although in an equivalent scalar-tensor cosmological setup the scalar field interacts with the fluid (which we consider to be the pressureless dust). Determining the conditions for the existence of the stable critical points we check their physical viability, in both Einstein and Jordan frames. We also verify that in either of these frames, the evolution of the universe at the corresponding stable points matches with that given by the respective exact solutions we have found in an earlier work (arXiv: 1611.00654 [gr-qc]). We not only examine the regions of physical relevance for the trajectories in the phase space when the coupling parameter is varied, but also demonstrate the evolution profiles of the cosmological parameters of interest along fiducial trajectories in the effectively non-interacting scenarios, in both Einstein and Jordan frames.