Phase space analysis of interacting dark energy in f(T) cosmology

TL;DR

This paper analyzes the phase space dynamics of interacting dark energy within f(T) cosmology, identifying attractor solutions and stability conditions for specific models and coupling parameters.

Contribution

It introduces a phase space analysis of interacting dark energy in f(T) cosmology, revealing attractor solutions and stability conditions for specific forms of f(T).

Findings

Existence of one attractor solution in the dynamical system.

Critical points lie on a specific sheet in phase space.

Coupling parameter c is constrained to (-2,0).

Abstract

In this paper, we examine the interacting dark energy model in $f(T)$ cosmology. We assume dark energy as a perfect fluid and choose a specific cosmologically viable form $f(T)= \beta\sqrt{T} $. We show that there is one attractor solution to the dynamical equation of $f(T)$ Friedmann equations. Further we investigate the stability in phase space for a general $f(T)$ model with two interacting fluids. By studying the local stability near the critical points, we show that the critical points lie on the sheet $u^*=(c-1)v^*$ in the phase space, spanned by coordinates $(u,v,\Omega,T)$. From this critical sheet, we conclude that the coupling between the dark energy and matter $c\in (-2,0)$.