Effects of the quantisation ambiguities on the Big Bounce dynamics

TL;DR

This paper studies how different choices in the quantisation process of loop quantum cosmology affect the universe's bounce dynamics, revealing new phenomena like curvature singularities and oscillating models with no initial or final singularities.

Contribution

It systematically analyzes the impact of quantisation ambiguities on the Big Bounce scenario using dynamical systems methods in loop quantum cosmology.

Findings

Positive cosmological constant leads to oscillating, non-singular models.

Curvature singularities can occur but are avoidable with positive cosmological constant.

Negative cosmological constant results in asymptotic Einstein static universe states.

Abstract

In this paper we investigate dynamics of the modified loop quantum cosmology models using dynamical systems methods. Modifications considered come from the choice of the different field strength operator $\hat{F}$ and result in different forms of the effective Hamiltonian. Such an ambiguity of the choice of this expression from some class of functions is allowed in the framework of loop quantisation. Our main goal is to show how such modifications can influence the bouncing universe scenario in the loop quantum cosmology. In effective models considered we classify all evolutional paths for all admissible initial conditions. The dynamics is reduced to the form of a dynamical system of the Newtonian type on a 2-dimensional phase plane. These models are equivalent dynamically to the FRW models with the decaying effective cosmological term parametrised by the canonical variable $p$ (or by the scale factor $a$). We find that for the positive cosmological constant there is a class of oscillating models without the initial and final singularities. The new phenomenon is the appearance of curvature singularities for the finite values of the scale factor, but we find that for the positive cosmological constant these singularities can be avoided. For the positive cosmological constant the evolution begins at the asymptotic state in the past represented by the deSitter contracting (deS$_{-}$) spacetime or the static Einstein universe H=0 or $H=-\infty$ state and reaches the deSitter expanding state (deS$_{+}$), the state H=0 or $H=+\infty$ state. In the case of the negative cosmological constant we obtain the past and future asymptotic states as the Einstein static universes.