Loop quantum cosmological model from ADM Hamiltonian

TL;DR

This paper derives a loop quantum cosmology model from the ADM Hamiltonian for a flat FRW universe, revealing a lower critical density for the bounce, which implies earlier quantum gravity effects and easier detection.

Contribution

It introduces a new LQC model based on the ADM Hamiltonian with a significantly reduced critical density for the bounce.

Findings

Critical density for bounce is a quarter of the previous model.

Modified Friedmann equation retains the same form as APS LQC.

Quantum gravity effects become detectable earlier.

Abstract

The loop quantum cosmological model from ADM Hamiltonian is studied in this paper. We consider the spatially flat homogeneous FRW model. It turns out that the modified Friedmann equation keeps the same form as the APS LQC model. However, the critical matter density for the bounce point is only a quarter of the previous APS model, i.e. $\rho_{cL}=\frac{\rho_c}{4}$. This is interesting because the lower critical bounce density means the quantum gravity effects will get involved earlier than the previous LQC model. Besides, the lower critical density also means the detection of quantum gravity effects easier than the previous model.