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, 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 ${\varphi }^2$ 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.

arXiv comment25 pages, 10 figures

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• Health checkup test of the standard cosmological model in view of recent Cosmic Microwave Background Anisotropies experiments
• Cosmological constraints on slow-roll inflation: an update
• The resilience of the Etherington-Hubble relation
• Phenomenological implications of modified loop cosmologies: an overview
• Quantum gravity might restrict a cyclic evolution
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• Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications
• Tilted non-spatially-flat inflation
• Alternative effective mass functions in the modified Mukhanov-Sasaki equation of loop quantum cosmology
• On the role of dissipative effects in the quantum gravitational onset of warm Starobinsky inflation in a closed universe