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

Understand

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.