Positive cosmological constant in loop quantum cosmology

TL;DR

This paper investigates the effects of a positive cosmological constant in loop quantum cosmology, showing that the big bang singularity is replaced by a bounce and that quantum evolution is robust against certain mathematical ambiguities.

Contribution

It demonstrates that in LQC with a positive cosmological constant, the big bounce persists regardless of self-adjoint extension choices, revealing a potential general property of quantum operators.

Findings

Big bang singularity is replaced by a big bounce in LQC.

Quantum evolution is insensitive to self-adjoint extension choices.

Classical universe expands to infinite proper time with zero matter density.

Abstract

The k=0 Friedmann Lemaitre Robertson Walker model with a positive cosmological constant and a massless scalar field is analyzed in detail. If one uses the scalar field as relational time, new features arise already in the Hamiltonian framework of classical general relativity: In a finite interval of relational time, the universe expands out to infinite proper time and zero matter density. In the deparameterized quantum theory, the true Hamiltonian now fails to be essentially self-adjoint both in the Wheeler DeWitt (WDW) approach and in LQC. Irrespective of the choice of the self-adjoint extension, the big bang singularity persists in the WDW theory while it is resolved and replaced by a big bounce in loop quantum cosmology (LQC). Furthermore, the quantum evolution is surprisingly insensitive to the choice of the self-adjoint extension. This may be a special case of an yet to be discovered general property of a certain class of symmetric operators that fail to be essentially self-adjoint.