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Loop Quantum Gravity on Dynamical Lattice and Improved Cosmological Effective Dynamics

Jan 20
Group Seminar
1:00 pm o'clock to 2:30 pm o'clock
Hongguang Liu (FAU Erlangen, Germany)

We propose a new approach to allow the spatial cubic lattice (graph) to change dynamically in the physical time evolution in the framework of path integral formulation of the reduced phase space LQG. When we focus on solutions with homogeneous and isotropic symmetry, the effective dynamics of cosmology are given by the equations of motion of the path integral derived from the full LQG. The resulting cosmological effective dynamics with the dynamical lattice improves the effective dynamics obtained earlier from the path integral with fixed spatial lattice, with results qualitatively similar to the properties of $bar{mu}$-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 will also discuss the cosmological perturbation theory on the dynamical lattice, and the relation to the Mukhanov-Sasaki equation.