Quantum gravitational onset of Starobinsky inflation in a closed
  universe
  Recent cosmic microwave background observations favor low energy scale
inflationary models in a closed universe. However, onset of inflation in such
models for a closed universe is known to be severely problematic. In
particular, such a universe recollapses within a few Planck seconds and
encounters a big crunch singularity when initial conditions are given in the
Planck regime. We show that this problem of onset of inflation in low energy
scale inflationary models can be successfully overcome in a quantum
gravitational framework where the big bang/big crunch singularities are
resolved and a non-singular cyclic evolution exists prior to inflation. As an
example we consider a model in loop quantum cosmology and demonstrate that the
successful onset of low energy scale inflation in a closed universe is possible
for the Starobinsky inflationary model starting from a variety of initial
conditions where it is impossible in the classical theory. For comparison we
also investigate the onset of inflation in the $\phi^2$ inflationary model
under similar unfavorable conditions. The pre-inflationary phase with quantum
gravity effects is shown to be composed of non-identical cycles of bounces and
recollapses resulting in a hysteresis-like phenomenon, which plays an important
role in creating suitable conditions for inflation to occur after some number
of non-singular cycles. Our analysis shows that the tension in the classical
theory amounting to the unsuitability of closed FLRW universes with respect to
the onset of low energy scale inflation can be successfully resolved in loop
quantum cosmology.
