Non-Singular Bouncing Universes in Loop Quantum Cosmology

TL;DR

Loop Quantum Cosmology predicts non-singular bouncing universes due to quantum geometric effects, allowing for consistent inflationary and cyclic models without singularities or energy condition violations.

Contribution

This paper demonstrates that LQC's quantum effects lead to generic bounces and enables the construction of non-singular cyclic models with minor potential modifications.

Findings

Quantum effects induce a bounce at Planck-scale densities.

Inflationary trajectories are attractors post-bounce.

Cyclic models can be non-singular with slight potential adjustments.

Abstract

Non-perturbative quantum geometric effects in Loop Quantum Cosmology predict a $\rho^2$ modification to the Friedmann equation at high energies. The quadratic term is negative definite and can lead to generic bounces when the matter energy density becomes equal to a critical value of the order of the Planck density. The non-singular bounce is achieved for arbitrary matter without violation of positive energy conditions. By performing a qualitative analysis we explore the nature of the bounce for inflationary and Cyclic model potentials. For the former we show that inflationary trajectories are attractors of the dynamics after the bounce implying that inflation can be harmoniously embedded in LQC. For the latter difficulties associated with singularities in cyclic models can be overcome. We show that non-singular cyclic models can be constructed with a small variation in the original Cyclic model potential by making it slightly positive in the regime where scalar field is negative.