Abstract
The loop quantum cosmological model from ADM Hamiltonian is studied in this article. 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, that is, ρcL=ρc4. 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.
Highlights
Loop quantum gravity (LQG) is a quantum gravity model which is trying to quantize Einstein’s general relativity (GR) by using background independent techniques
The loop quantum cosmological model which consists of the purely Lorentzian term is studied in this article
It turns out that the modified Friedmann equation keeps the same form as the APS loop quantum cosmology (LQC) model
Summary
Loop quantum gravity (LQG) is a quantum gravity model which is trying to quantize Einstein’s general relativity (GR) by using background independent techniques. In the recently proposed model, different from the Ashtekar-PawlowskiSingh (APS) model (Ashtekar et al, 2006b), one treats the so-called Euclidean term and Lorentzianian term of the Hamiltonian constraint independently (Yang et al, 2009; Assanioussi et al, 2018). It was shown in the study by Assanioussi et al (2018); Assanioussi et al (2019) that this model can lead to a new de Sitter epoch evolution scenario where the prebounce geometry could be described at the effective level. Conclusion and some outlook are presented in the last section
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