Numerical Analysis of the Big Bounce in Loop Quantum Cosmology

Abstract

Loop quantum cosmology homogeneous models with a massless scalar field show that the big-bang singularity can be replaced by a big quantum bounce. To gain further insight on the nature of this bounce, we study the semi-discrete loop quantum gravity Hamiltonian constraint equation from the point of view of numerical analysis. For illustration purposes, we establish a numerical analogy between the quantum bounces and reflections in finite difference discretizations of wave equations triggered by the use of nonuniform grids or, equivalently, reflections found when solving numerically wave equations with varying coefficients. We show that the bounce is closely related to the method for the temporal update of the system and demonstrate that explicit time-updates in general yield bounces. Finally, we present an example of an implicit time-update devoid of bounces and show back-in-time, deterministic evolutions that reach and partially jump over the big-bang singularity.

5 pages, 3 figures, new title, replaced with version accepted for publication

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• Loop Quantum Cosmology: A Status Report
• Robustness of key features of loop quantum cosmology
• Large scale effective theory for cosmological bounces
• Numerical loop quantum cosmology: an overview
• Non-singular Bounce Cosmology from Lagrange Multiplier $F(R)$ Gravity
• Numerical Techniques in Loop Quantum Cosmology
• The Raychaudhuri equation for a quantized timelike geodesic congruence
• Quantum no-singularity theorem from geometric flows
• Viable non-singular cosmic bounce in holonomy improved F(R) gravity endowed with a Lagrange multiplier
• Pre-big bang collapsing universe from modern Kaluza-Klein theory of gravity
• A Universe from a Lagrangian Fixed Point