# Generic absence of strong singularities and geodesic completeness in modified loop quantum cosmologies

## TL;DR

This paper demonstrates that modified loop quantum cosmologies (mLQC-I and mLQC-II) avoid strong singularities and are geodesically complete, although some pressure singularities may still occur without causing geodesic breakdown.

## Contribution

It provides a comprehensive analysis of singularity resolution in modified loop quantum cosmologies, highlighting differences from standard loop quantum cosmology and showing the persistence of certain weak singularities.

## Key findings

- Volume remains finite and non-zero during evolution.
- Big rip and big freeze singularities are resolved.
- Sudden and type-IV singularities are not resolved.

## Abstract

Different regularizations of the Hamiltonian constraint in loop quantum cosmology yield modified loop quantum cosmologies, namely mLQC-I and mLQC-II, which lead to qualitatively different Planck scale physics. We perform a comprehensive analysis of resolution of various singularities in these modified loop cosmologies using effective spacetime description and compare with earlier results in standard loop quantum cosmology. We show that the volume remains non-zero and finite in finite time evolution for all considered loop cosmological models. Interestingly, even though expansion scalar and energy density are bounded due to quantum geometry, curvature invariants can still potentially diverge due to pressure singularities at a finite volume. These divergences are shown to be harmless since geodesic evolution does not break down and no strong singularities are present in the effective spacetimes of loop cosmologies. Using a phenomenological matter model, various types of exotic strong and weak singularities, including big rip, sudden, big freeze and type-IV singularities, are studied. We show that as in standard loop quantum cosmology, big rip and big freeze singularities are resolved in mLQC-I and mLQC-II, but quantum geometric effects do not resolve sudden and type-IV singularities.