Bounce inflation in $f(T)$ Cosmology: A unified inflaton-quintessence
  field
  We investigate a bounce inflation model with a graceful exit into the
Friedmann-Robertson-Walker (FRW) decelerated Universe within $f(T)$ gravity
framework, where $T$ is the torsion scalar in the teleparallelism. We study the
cosmic thermal evolution, the model predicts a supercold Universe during the
precontraction phase, which is consistent with the requirements of the
slow-roll models, while it performs a reheating period by the end of the
contraction with a maximum temperature just below the grand unified theory
(GUT) temperature. However, it matches the radiation temperature of the hot big
bang at later stages. The equation-of-state due to the effective gravitational
sector suggests that our Universe is self-accelerated by teleparallel gravity.
We assume the matter component to be a canonical scalar field. We obtain the
scalar field potential that is induced by the $f(T)$ theory. The power spectrum
of the model is nearly scale invariant. In addition, we show that the model
unifies inflaton and quintessence fields in a single model. Also, we revisited
the primordial fluctuations in $f(T)$ bounce cosmology, to study the
fluctuations that are produced at the precontraction phase.
