Exact solutions for Big Bounce in loop quantum cosmology

TL;DR

This paper derives exact analytical solutions for flat loop quantum cosmology models with a scalar field and cosmological constant, revealing oscillatory universes without singularities across various configurations.

Contribution

It provides explicit solutions and analyzes the impact of the cosmological constant on the dynamics of loop quantum cosmology models.

Findings

Oscillating solutions without singularities are generic for some quantization schemes.

The cosmological constant influences the qualitative behavior of solutions.

Explicit analytical solutions are obtained for different configurations.

Abstract

In this paper we study the flat (k=0) cosmological FRW model with holonomy corrections of Loop Quantum Gravity. The considered universe contains a massless scalar field and the cosmological constant Lambda. We find analytical solutions for this model in different configurations and investigate its dynamical behaviour in the whole phase space. We show the explicit influence of Lambda on the qualitative and quantitative character of solutions. Even in the case of positive Lambda the oscillating solutions without the initial and final singularity appear as a generic case for some quantisation schemes.