Non-parametric reconstruction of an inflaton potential from
  Einstein-Cartan-Sciama-Kibble gravity with particle production
  The coupling between spin and torsion in the Einstein-Cartan-Sciama-Kibble
theory of gravity generates gravitational repulsion at very high densities,
which prevents a singularity in a black hole and may create there a new
universe. We show that quantum particle production in such a universe near the
last bounce, which represents the Big Bang gives the dynamics that solves the
horizon, flatness, and homogeneity problems in cosmology. For a particular
range of the particle production coefficient, we obtain a nearly constant
Hubble parameter that gives an exponential expansion of the universe with more
than 60 $e$-folds, which lasts about $\sim 10^{-42}$ s. This scenario can thus
explain cosmic inflation without requiring a fundamental scalar field and
reheating. From the obtained time dependence of the scale factor, we follow the
prescription of Ellis and Madsen to reconstruct in a non-parametric way a
scalar field potential which gives the same dynamics of the early universe.
This potential gives the slow-roll parameters of cosmic inflation, from which
we calculate the tensor-to-scalar ratio, the scalar spectral index of density
perturbations, and its running as functions of the production coefficient. We
find that these quantities do not significantly depend on the scale factor at
the Big Bounce. Our predictions for these quantities are consistent with the
Planck 2015 observations.
