Smooth Big Bounce from Affine Quantization

TL;DR

This paper explores a novel quantum approach using affine coherent states to resolve gravitational singularities in a simple cosmological model, leading to a smooth big bounce instead of a singularity.

Contribution

It introduces an affine quantization method for cosmology that regularizes singularities and ensures well-defined quantum evolution, differing from traditional canonical quantization.

Findings

Quantum centrifugal potential regularizes singularity

Hamiltonian becomes essentially self-adjoint

Results suggest a smooth big bounce replaces the classical singularity

Abstract

We examine the possibility of dealing with gravitational singularities on a quantum level through the use of coherent state or wavelet quantization instead of canonical quantization. We consider the Robertson-Walker metric coupled to a perfect fluid. It is the simplest model of a gravitational collapse and the results obtained here may serve as a useful starting point for more complex investigations in future. We follow a quantization procedure based on affine coherent states or wavelets built from the unitary irreducible representation of the affine group of the real line with positive dilation. The main issue of our approach is the appearance of a quantum centrifugal potential allowing for regularization of the singularity, essential self-adjointness of the Hamiltonian, and unambiguous quantum dynamical evolution.