Loop quantum gravity effects might restrict a cyclic evolution

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It is generally expected that in a nonsingular 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 counterexample to this conventional wisdom. Working in the realm of loop cosmological models with nonperturbative 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 nonsingular 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 nonsingular 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 prebounce regime, but can be striking and profound even in the postbounce regime.

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