Alternative quantization of the Hamiltonian in isotropic loop quantum cosmology

TL;DR

This paper investigates a different way of quantizing the Hamiltonian in isotropic loop quantum cosmology and finds that key features like the quantum bounce remain robust despite the ambiguity.

Contribution

It introduces an alternative Hamiltonian constraint operator considering a specific quantization ambiguity and demonstrates its classical limit and quantum effects.

Findings

Quantum bounce persists with the alternative quantization.

The effective Hamiltonian includes higher order quantum corrections.

The possibility of recollapse remains due to quantum gravity effects.

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, such as the quantum bounce and effective scenario, are robust against the ambiguities. In this paper, we consider a typical quantization ambiguity arising from the quantization of the field strength of the gravitational connection. An alternative Hamiltonian constraint operator is constructed, which is shown to have the correct classical limit by the semiclassical analysis. The effective Hamiltonian incorporating higher order quantum corrections is also obtained. In the spatially flat FRW model with a massless scalar field, the classical big bang is again replaced by a quantum bounce. Moreover, there are still great possibilities for the expanding universe to recollapse due to the quantum gravity effect. Thus, these key features are robust against this quantization ambiguity.