  A cubic correction of $f(T)$ gravity, where $T$ is the teleparallel scalar
torsion, is considered to describe gravity in spatially flat
Friedmann-Robertson-Walker model. A scale factor permitting departure from
inflation era has been derived. The cosmological evolution has been studied and
it has shown that a phase transition from early era to late one is possible.
The maximum temperature by releasing the vacuum latent heat has been shown to
be much below the GUT temperature. The energy conditions have been analyzed and
has shown that they are satisfied for certain values of the parameters
$\varepsilon$ and $\beta$. The cosmographic parameters are used and has been
shown that the derived solution satisfies $f(T)$ and its higher derivatives up
to fourth order.
