A Built-in Inflation in the $f(T)$-Cosmology
  In the present work we derive an exact solution of an isotropic and
homogeneous Universe governed by $f(T)$ gravity. We show how the torsion
contribution to the FRW cosmology can provide a \textit{unique} origin for both
early and late acceleration phases of the Universe. The three models ($k=0, \pm
1$) show a \textit{built-in} inflationary behavior at some early Universe time;
they restore suitable conditions for the hot big bang nucleosynthesis to begin.
Unlike the standard cosmology, we show that even if the Universe initially
started with positive or negative sectional curvatures, the curvature density
parameter enforces evolution to a flat Universe. The solution constrains the
torsion scalar $T$ to be a constant function at all time $t$, for the three
models. This eliminates the need for the dark energy (DE). Moreover, when the
continuity equation is assumed for the torsion fluid, we show that the flat and
closed Universe models \textit{violate} the conservation principle, while the
open one does not. The evolution of the effective equation of state (EoS) of
the torsion fluid implies a peculiar trace from a quintessence-like DE to a
phantom-like one crossing a matter and radiation EoS in between; then it
asymptotically approaches a de Sitter fate.
