The Big-Bang Singularity in the framework of a Generalized Uncertainty Principle

TL;DR

This paper investigates how a Generalized Uncertainty Principle affects the quantum dynamics of the early universe, suggesting a non-singular evolution without a Big Bounce, contrasting with Loop Quantum Cosmology predictions.

Contribution

It introduces a quantization approach based on an extended Heisenberg algebra to analyze the universe's initial singularity within a GUP framework.

Findings

Non-singular universe evolution observed

Absence of a Big Bounce indicated

Probability density remains well-behaved near the singularity

Abstract

We analyze the quantum dynamics of the Friedmann-Robertson-Walker Universe in the context of a Generalized Uncertainty Principle. Since the isotropic Universe dynamics resembles that of a one-dimensional particle, we quantize it with the commutation relations associated to an extended formulation of the Heisenberg algebra. The evolution of the system is described in terms of a massless scalar field taken as a relational time. We construct suitable wave packets and analyze their dynamics from a quasi-classical region to the initial singularity. The appearance of a non singular dynamics comes out as far as the behavior of the probability density is investigated. Furthermore, reliable indications arise about the absence of a Big-Bounce, as predicted in recent issues of Loop Quantum Cosmology.