2021/01/19 by Muxin Han, Hongguang Liu · 1 citation
Medicine · Physics and Astronomy · #Black Holes and Theoretical Physics #De Sitter universe #Initial singularity #Loop quantum cosmology #Loop quantum gravity #Mathematical physics #Neuroblastoma Research and Treatments #Noncommutative and Quantum Gravity Theories #Path integral formulation #Physics #Quantum #Quantum gravity #Quantum mechanics #Scalar field #Spacetime #Universe #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.104.024011
published as Phys. Rev. D 104, 024011 (2021) · 44 pages, 17 figures
arxiv created 2021/01/19 · openalex publication_date 2021/07/06 · arxiv updated 2021/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
In the path integral formulation of the reduced phase space loop quantum gravity (LQG), we propose a new approach to allow the spatial cubic lattice (graph) to change dynamically in the physical time evolution. The equations of motion of the path integral derive the effective dynamics of cosmology from the full LQG, when we focus on solutions with homogeneous and isotropic symmetry. The resulting cosmological effective dynamics with the dynamical lattice improves the effective dynamics obtained earlier from the path integral with a fixed spatial lattice: The improved effective dynamics recovers the Friedmann-Lema\\itre-Robertson-Walker cosmology at low energy density and resolves the big-bang singularity with a bounce. The critical density \ensuremathρc at the bounce is Planckian \ensuremathρc\ensuremath∼\mathrm\ensuremathΔ^\ensuremath-1, where \mathrm\ensuremathΔ is a Planckian area serving as a certain UV cutoff of the effective theory. The effective dynamics gives the unsymmetric bounce and has the de Sitter (dS) spacetime in the past of the bounce. The cosmological constant \mathrm\ensuremathΛeff of the dS spacetime is emergent from the quantum effect \mathrm\ensuremathΛeff\ensuremath∼\mathrm\ensuremathΔ^\ensuremath-1. These results are qualitatively similar to the properties of \ensuremathμ-scheme loop quantum cosmology. Moreover, we generalize the earlier path integral formulation of the full LQG by taking into account the coupling with an additional real scalar field, which drives the slow-roll inflation of the effective cosmological dynamics. In addition, we discuss the cosmological perturbation theory on the dynamical lattice and the relation to the Mukhanov-Sasaki equation.