Unitary evolution and cosmic acceleration in Loop Quantum Cosmology

TL;DR

This paper investigates the conditions for unitary evolution in Loop Quantum Cosmology with arbitrary Hamiltonian weights, emphasizing the necessity of self-adjoint extensions for positive weights to match cosmological observations.

Contribution

It extends previous work by analyzing unitary evolution in Loop Quantum Cosmology for arbitrary weights, highlighting the importance of self-adjoint extensions for positive weights.

Findings

Unitary evolution holds for non-positive weights without extensions.

Self-adjoint extensions are necessary for positive weights to ensure unitarity.

Extensions are implemented via a propagator to match observational data.

Abstract

Loop quantum cosmology was shown to interpolate between de Sitter and FLRW Universe phases through a bounce by including Euclidean and Lorentzian terms of the Hamiltonian constraint with weight one -that corresponding to classical General Relativity. Unitary evolution required self-adjoint extensions of the constraint and a Planckian cosmological constant was obtained. Independent work took a positive weight to get a cosmological constant with the observed value, without considering unitarity. In this work we address the unitary evolution of the model for arbitrary weight. For non positive weight parameter unitary holds but for positive values self-adjoint extensions are required. To encompass observations the extensions here provided are mandatory. These are implemented in a propagator. Finally, we discuss our results and perspectives.