Emerging singularities in the bouncing loop cosmology

Abstract

In this paper we calculate $\mathcal{O}({\mu }^4)$ corrections from holonomies in the Loop Quantum Gravity, usually not taken into account. Allowance of the corrections of this kind is equivalent with the choice of the new quatization scheme. Quantization ambiguities in the Loop Quantum Cosmology allow for this additional freedom and presented corrections are consistent with the standard approach. We apply these corrections to the flat FRW cosmological model and calculate the modified Friedmann equation. We show that the bounce appears in the models with the standard $\mathcal{O}({\mu }^2)$ quantization scheme is shifted to the higher energies ${\rho }_{\text{bounce}}=3{\rho }_{\text{c}}$. Also a pole in the Hubble parameter appears for ${\rho }_{\text{pole}}=3/2{\rho }_{\text{c}}$ corresponding to \emph{hyper-inflation/deflation} phases. This pole represents a curvature singularity at which the scale factor is finite. In this scenario the singularity and bounce co-exist. Moreover we find that an ordinary bouncing solution appears only when quantum corrections in the lowest order are considered. Higher order corrections can lead to the nonperturbative effects.

RevTeX4, 8 pages, 4 figures; v2 change of title, more discussion on co-existence of singularity and bounce

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