Cosmological viability conditions for $f(T)$ dark energy models

TL;DR

This paper analyzes the conditions under which $f(T)$ gravity models can produce realistic cosmological evolution, identifying viable trajectories that include radiation, matter, and accelerated expansion phases.

Contribution

It provides a detailed dynamical analysis of $f(T)$ models, establishing geometric viability conditions and examining the evolution paths of these dark energy models.

Findings

Two viable cosmological trajectories identified with realistic evolution sequences.

Conditions for the universe to pass through radiation, matter, and accelerated phases.

Certain $f(T)$ models are shown to be incompatible with observed cosmic evolution.

Abstract

Recently $f(T)$ modified teleparallel gravity where T is the torsion scalar has been proposed as the natural gravitational alternative for dark energy. We perform a detailed dynamical analysis of these models and find conditions for the cosmological viability of $f(T)$ dark energy models as geometrical constraints on the derivatives of these models. We show that in the phase space exists two cosmologically viable trajectory which (i) The universe would start from an unstable radiation point, then pass a saddle standard matter point which is followed by accelerated expansion de sitter point. (ii) The universe starts from a saddle radiation epoch, then falls onto the stable matter era and the system can not evolve to the dark energy dominated epoch. Finally, for a number of $f(T)$ dark energy models were proposed in the more literature, the viability conditions are investigated.