  It is shown that teleparallel $F(T)$ theories of gravity combined with
holonomy corrected Loop Quantum Cosmology (LQC) support a Matter Bounce
Scenario (MBS) which is a potential alternative to the inflationary paradigm.
The Matter Bounce Scenario is reviewed and, according to the current
observational data provided by PLANCK's team, we have summarized all the
conditions that it has to satisfy in order to be a viable alternative to
inflation, such as to provide a theoretical value of the spectral index and its
running compatible with the latest PLANCK data, to have a reheating process via
gravitational particle production, or to predict some signatures in the
non-gaussianities of the power spectrum. The calculation of the power spectrum
for scalar perturbations and the ratio of tensor to scalar perturbations has
been done, in the simplest case of an exact matter dominated background, for
both holonomy corrected LQC and teleparallel $F(T)$ gravity. Finally, we have
discussed the challenges (essentially, dealing with non-gaussianities, the
calculation of the 3-point function in flat spatial geometries for theories
beyond General Relativity) and problems (Jeans instabilities in the case of
holonomy corrected LQC or local Lorentz dependence in teleparallelism) that
arise in either bouncing scenario.
