Algorithmic approach to Cosmological Coherent State Expectation Values in LQG

Abstract

In the lattice approach to Loop Quantum Gravity on a fixed graph computations tend to be involved and are rarely analytically manageable. But, when interested in the expectation values of coherent states on the lattice which are sharply peaked on isotropic, flat cosmology several simplifications are possible which reduce the computational effort. We present a step-by-step algorithm resulting in an analytical expression including up to first order corrections in the spread of the state. The algorithm is developed in such a way that it makes the computation straightforward and easy to be implementable in programming languages such as Mathematica. Exemplarily, we demonstrate how the algorithm streamlines the road to obtain the expectation value of the euclidean part of the scalar constraint and as a consistency check perform the analytic computation as well. To showcase further applications of the algorithm, we investigate the fate of the effective dynamics program custom in Loop Cosmology and find that the next-to-leading order corrections can {\it not} be used as corrections for an effective Hamiltonian.

arXiv comment33 pages; This paper summarizes the results announced at Loops'19 Conference [http://gravity.psu.edu/events/loops19/index-loops19.shtml]. First draft - minor typos can still be found

References in corpus (38)

• Quantum Nature of the Big Bang
• Quantum Spin Dynamics (QSD)
• Loop Quantum Cosmology
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Quantum Spin Dynamics (QSD) II
• Gauge Field Theory Coherent States (GCS) : I. General Properties
• Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties
• Loop Quantum Cosmology: An Overview
• Algebraic Quantum Gravity (AQG) I. Conceptual Setup
• Scalar Material Reference Systems and Loop Quantum Gravity
• Improved and Perfect Actions in Discrete Gravity
• Gauge Field Theory Coherent States (GCS) : III. Ehrenfest Theorems
• Effective loop quantum gravity framework for vacuum spherically symmetric space-times
• Quantum Spin Dynamics (QSD) : VII. Symplectic Structures and Continuum Lattice Formulations of Gauge Field Theories
• Coherent spin-networks
• Quantum-Reduced Loop Gravity: Cosmology
• Emergent de Sitter epoch of the quantum Cosmos
• Algebraic Quantum Gravity (AQG) II. Semiclassical Analysis
• A Real Polynomial Formulation of General Relativity in terms of Connections
• Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
• New scalar constraint operator for loop quantum gravity
• Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
• Cosmological Coherent State Expectation Values in LQG I. Isotropic Kinematics
• Hamiltonian Renormalisation I: Derivation from Osterwalder-Schrader Reconstruction
• Quantum Reduced Loop Gravity: a realistic Universe
• Group Averaging and Refined Algebraic Quantization: Where are we now?
• Quantum spin dynamics
• Quantum Spacetime on a Quantum Simulator
• Observational consequences of Bianchi I spacetimes in loop quantum cosmology
• Twisted Geometries Coherent States for Loop Quantum Gravity
• Effective dynamics of the Schwarzschild black hole interior with inverse triad corrections
• Efficient Simulation of Loop Quantum Gravity -- A Scalable Linear-Optical Approach
• Quantum simulations of a qubit of space
• Challenges in recovering a consistent cosmology from the effective dynamics of loop quantum gravity
• Operators of quantum-reduced loop gravity from the perspective of full loop quantum gravity
• The time-dependent mass of cosmological perturbations in loop quantum cosmology: Dapor-Liegener regularization
• Stable coherent states
• Expectation values of Coherent States for $\mathrm{SU}(2)$ Lattice Gauge Theories

Cited by in corpus (5)

• Shadow and stability of quantum-corrected black holes
• First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian
• Fermions in Loop Quantum Gravity and Resolution of Doubling Problem
• Alternative $k=-1$ loop quantum cosmology
• Quantum speed limit and stability of coherent states in quantum gravity