Numerical analysis of the big bounce in loop quantum cosmology

Pablo Laguna
Phys. Rev. D 75, 024033 – Published 25 January 2007

Abstract

Loop quantum cosmology (LQC) 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 semidiscrete 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.

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  • Received 28 August 2006

DOI:https://doi.org/10.1103/PhysRevD.75.024033

©2007 American Physical Society

Authors & Affiliations

Pablo Laguna*

  • Department of Astronomy and Astrophysics, Penn State University, University Park, Pennsylvania 16802, USA

  • *Also at IGPG, CGWP, Physics Department.

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Issue

Vol. 75, Iss. 2 — 15 January 2007

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