$f(T)$ Cosmology with Nonzero Curvature

Understand

We investigate exact and analytic solutions in $f\left( T\right) $ gravity within the context of a Friedmann--Lema\^{\i}tre--Robertson--Walker background space with nonzero spatial curvature.

• For the power law theory $f\left( T\right) =T^{n}$ we find that the field equations admit an exact solution with a linear scalar factor for negative and positive spatial curvature.
• That Milne-like solution is asymptotic behaviour for the scale factor near the initial singularity for the model $f\left( T\right) =T+f_{0}T^{n}-2\Lambda$.
• The analytic solution for that specific theory is presented in terms of Painlev\'{e} Series for $n>1$.