Quantum gravitational onset of Starobinsky inflation in a closed universe

Abstract

Recent cosmic microwave background observations favor low-energy-scale inflationary models in a closed universe. However, the 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 the 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 nonsingular 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 ${\ensuremath{\phi}}^{2}$ inflationary model under highly unfavorable conditions and find similar results. Our numerical investigation including the phase-space analysis shows that the preinflationary phase with quantum gravity effects is composed of nonidentical 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 nonsingular cycles. Our analysis shows that the tension in the classical theory amounting to the unsuitability of closed Friedmann-Lema\^{\i}tre-Robertson-Walker universes with respect to the onset of low-energy-scale inflation can be successfully resolved in loop quantum cosmology.