Alternative quantization of the Hamiltonian in loop quantum cosmology II: Including the Lorentz term

TL;DR

This paper explores alternative methods for quantizing the Lorentz term in loop quantum cosmology, demonstrating that key features like the quantum bounce and potential recollapse remain robust across different quantization schemes.

Contribution

It introduces two new approaches to quantize the Lorentz term, aligning more closely with full loop quantum gravity, and shows these preserve the core features of loop quantum cosmology.

Findings

Quantum bounce replaces classical big bang.

Both schemes produce correct classical limits.

Quantum effects may cause universe recollapse.

Abstract

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology are robust against the ambiguities. In this paper, we quantize the Lorentz term of the gravitational Hamiltonian constraint in the spatially flat FRW model by two approaches different from that of the Euclidean term. One of the approaches is very similar to the treatment of the Lorentz part of Hamiltonian in loop quantum gravity and hence inherits more features from the full theory. Two symmetric Hamiltonian constraint operators are constructed respectively in the improved scheme. Both of them are shown to have the correct classical limit by the semiclassical analysis. In the loop quantum cosmological model with a massless scalar field, the effective Hamiltonians and Friedmann equations are derived. It turns out that the classical big bang is again replaced by a quantum bounce in both cases. Moreover, there are still great possibilities for the expanding universe to recollapse due to the quantum gravity effect.