Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity

Abstract

A new routine is proposed to relate Loop Quant Cosmology (LQC) to Loop Quantum Gravity (LQG) from the perspective of effective dynamics. We derive the big-bang singularity resolution and big bounce from the first principle of full canonical LQG. Our results are obtained in the framework of the reduced phase space quantization of LQG. As a key step in our work, we derive with coherent states a new discrete path integral formula of the transition amplitude generated by the physical Hamiltonian. The semiclassical approximation of the path integral formula gives an interesting set of effective equations of motion (EOMs) for full LQG. When solving the EOMs with homogeneous and isotropic ansatz, we reproduce the LQC effective dynamics in ${\mu }_0$-scheme. The solution replaces the big-bang singularity by a big bounce. In the end, we comment on the possible relation between the $\bar{\mu }$-scheme of effective dynamics and the continuum limit of the path integral formula.

30+10 pages, 2 figures

References in corpus (19)

• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Are loop quantum cosmos never singular?
• Loop Quantum Cosmology: An Overview
• Gravity quantized
• The length operator in Loop Quantum Gravity
• Stepping out of Homogeneity in Loop Quantum Cosmology
• New length operator for loop quantum gravity
• Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory
• Hamiltonian operator for loop quantum gravity coupled to a scalar field
• Relating loop quantum cosmology to loop quantum gravity: Symmetric sectors and embeddings
• A quantum reduction to Bianchi I models in loop quantum gravity
• Local spinfoam expansion in loop quantum cosmology
• Loop Quantum Cosmology: A brief review
• Bouncing evolution in a model of loop quantum gravity
• Quantum spin dynamics
• Coherent State Functional Integral in Loop Quantum Cosmology: Alternative Dynamics
• Cosmological dynamics in spin-foam loop quantum cosmology: challenges and prospects