paper

Quantum gravity might restrict a cyclic evolution

arXiv:2108.12553 · doi:10.1103/PhysRevD.105.046013

Abstract

It is generally expected that in a non-singular cosmological model a cyclic evolution is straightforward to obtain on introduction of a suitable choice of a scalar field with a negative potential or a negative cosmological constant which causes a recollapse at some time in the evolution. We present a counter example to this conventional wisdom. Working in the realm of loop cosmological models with non-perturbative quantum gravity modifications we show that a modified version of standard loop quantum cosmology based on Thiemann's regularization of the Hamiltonian constraint while generically non-singular does not allow a cyclic evolution unless some highly restrictive conditions hold. Irrespective of the energy density of other matter fields, a recollapse and hence a cyclic evolution is only possible if one chooses an almost Planck sized negative potential of the scalar field or a negative cosmological constant. Further, cycles when present do not occur in the classical regime. Surprisingly, a necessary condition for a cyclic evolution, not singularity resolution, turns out to be a violation of the weak energy condition. These results are in a striking contrast to standard loop quantum cosmology where obtaining a recollapse at large volumes and a cyclic evolution is straightforward, and, there is no violation of weak energy condition. On one hand our work shows that some quantum cosmological models even though non-singular and bouncing are incompatible with a cyclic evolution, and on the other hand demonstrates that differences in various quantization prescriptions in loop cosmology need not be faint and buried in the pre-bounce regime, but can be striking and profound even in the post-bounce regime.

23 pages, 10 figures

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