AUTHOR=Ding You , Zhang Xiangdong 

TITLE=Loop Quantum Cosmological Model From ADM Hamiltonian

JOURNAL=Frontiers in Astronomy and Space Sciences

VOLUME=8

YEAR=2022

URL=https://www.frontiersin.org/journals/astronomy-and-space-sciences/articles/10.3389/fspas.2021.805998

DOI=10.3389/fspas.2021.805998

ISSN=2296-987X

ABSTRACT=<p>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, <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi>L</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:mfrac></mml:math></inline-formula>. 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.</p>