Fermi-bounce Cosmology and scale invariant power-spectrum
  We develop a non-singular bouncing cosmology using a non-trivial coupling of general relativity to fermionic fields. The usual Big Bang singularity is avoided thanks to a negative energy density contribution from the fermions. Our theory is ghost-free since the fermionic operator that generates the bounce is equivalent to torsion, which has no kinetic terms. The physical system consists of standard general relativity plus a topological sector for gravity, and fermionic matter described by Dirac fields with a non-minimal coupling. We show that a scale invariant power-spectrum generated in the contracting phase can be recovered by suitable choices of fermion number density and bare mass, thus providing a possible alternative to the inflationary scenario. 
Stephon Alexander, Cosimo Bambi, Antonino Marciano and Leonardo   Modesto
gr-qc astro-ph.CO hep-th