The Hidden Flat Like Universe: Starobinsky-like inflation induced by
  f(T) gravity
  We study a single fluid component in a flat like universe (FLU) governed by
$f(T)$ gravity theories, where $T$ is the teleparallel torsion scalar. The FLU
model, regardless the value of the spatial curvature $k$, identifies a special
class of $f(T)$ gravity theories. Remarkably, the FLU $f(T)$ gravity does not
reduce to teleparallel gravity theory. In large Hubble spacetime the theory is
consistent with the inflationary universe scenario and respects the
conservation principle. The equation of state (EoS) evolves similarly in all
models $k=0, \pm 1$. We study the case when the torsion tensor is made of a
scalar field, which enables to derive a quintessence potential from the
obtained $f(T)$ gravity theory. The potential produces Starobinsky-like model
naturally without using a conformal transformation, with higher orders
continuously interpolate between Starobinsky and quadratic inflation models.
The slow-roll analysis shows double solutions so that for a single value of the
scalar tilt (spectral index) $n_{s}$ the theory can predict double
tensor-to-scalar ratios $r$ of $E$-mode and $B$-mode polarizations.
