Loop quantum cosmology from an alternative Hamiltonian. II. Including the Lorentzian term

TL;DR

This paper extends loop quantum cosmology by including the Lorentzian term in the Hamiltonian constraint, leading to a quantum bounce and an asymptotic de Sitter universe, thus improving the model's physical consistency.

Contribution

It introduces a new regularization scheme for the Lorentzian term in the Hamiltonian, aligning with full loop quantum gravity and analyzing its semiclassical limit.

Findings

Quantum bounce replaces classical singularity.

Backward evolution leads to an asymptotic de Sitter universe.

Negative energy density problem is resolved.

Abstract

The scheme of using the Chern-Simons action to regularize the gravitational Hamiltonian constraint is extended to including the Lorentzian term in the $k=0$ cosmological model. The Euclidean term and the Lorenzian term are thus regularized separately mimicking the treatment of full loop quantum gravity. The new quantum dynamics for the spatially flat Friedmann-Robertson-Walker model with a massless scalar field as an emergent time is studied. By semiclassical analysis, the effective Hamiltonian constraint is obtained, which indicates that the new quantum dynamics has the correct classical limit. The classical big-bang singularity is again replaced by a quantum bounce. Similar to the case of quantizing only the Euclidean term, the backward evolution of the cosmological model determined by the new effective Hamiltonian will be bounced to an asymptotic de Sitter universe coupled to a massless scalar field, while the problem of negative energy density of matter in the former case is resolved.