Singularities in loop quantum cosmology

TL;DR

This paper demonstrates that certain scalar field models in Loop Quantum Cosmology can lead to sudden curvature singularities, indicating limitations of the effective equations in fully resolving all types of cosmological singularities.

Contribution

It identifies specific conditions under which LQC's effective equations still produce singularities, highlighting the need for further refinement of the theory.

Findings

LQC avoids big bang and big rip singularities.

Sudden singularities with diverging Ricci scalar occur despite bounded Hubble rate.

Effective equations are insufficient to prevent all singularities.

Abstract

We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of Loop Quantum Cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude that the effective equations of LQC are not in themselves sufficient to avoid the occurrence of singularities.