Big bounce from spin and torsion
  The Einstein-Cartan-Sciama-Kibble theory of gravity naturally extends general
relativity to account for the intrinsic spin of matter. Spacetime torsion,
generated by spin of Dirac fields, induces gravitational repulsion in fermionic
matter at extremely high densities and prevents the formation of singularities.
Accordingly, the big bang is replaced by a bounce that occurred when the energy
density $\epsilon\propto gT^4$ was on the order of $n^2/m_\textrm{Pl}^2$ (in
natural units), where $n\propto gT^3$ is the fermion number density and $g$ is
the number of thermal degrees of freedom. If the early Universe contained only
the known standard-model particles ($g\approx 100$), then the energy density at
the big bounce was about 15 times larger than the Planck energy. The minimum
scale factor of the Universe (at the bounce) was about $10^{32}$ times smaller
than its present value, giving $\approx 50 \mum$. If more fermions existed in
the early Universe, then the spin-torsion coupling causes a bounce at a lower
energy and larger scale factor. Recent observations of high-energy photons from
gamma-ray bursts indicate that spacetime may behave classically even at scales
below the Planck length, supporting the classical spin-torsion mechanism of the
big bounce. Such a classical bounce prevents the matter in the contracting
Universe from reaching the conditions at which a quantum bounce could possibly
occur.
