# Loop quantum cosmology and singularities

## TL;DR

This paper analyzes singularities in loop quantum cosmology using the Bohmian formulation, showing that in certain models, big bang and big crunch singularities are avoided, unlike in Wheeler-DeWitt theory.

## Contribution

It applies the Bohmian formulation to loop quantum cosmology, demonstrating singularity avoidance in homogeneous and isotropic models with arbitrary curvature and cosmological constant.

## Key findings

- Singularities are avoided in the studied loop quantum cosmology models.
- Bohmian formulation predicts no singularities in these models.
- Contrast with Wheeler-DeWitt theory where singularities may occur.

## Abstract

Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.