Numerical Techniques in Loop Quantum Cosmology
arXiv:1110.0646 · doi:10.3842/SIGMA.2012.001
Abstract
In this article, we review the use of numerical techniques to obtain solutions for the quantum Hamiltonian constraint in loop quantum cosmology (LQC). First, we summarize the basic features of LQC, and describe features of the constraint equations to solve - generically, these are difference (rather than differential) equations. Important issues such as differing quantization methods, stability of the solutions, the semi-classical limit, and the relevance of lattice refinement in the difference equations are discussed. Finally, the cosmological models already considered in the literature are listed, along with typical features in these models and open issues.
References in corpus (37)
- Loop Quantum Cosmology: A Status Report
- Quantum Nature of the Big Bang: Improved dynamics
- Quantum Nature of the Big Bang
- Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
- Loop quantum cosmology of k=1 FRW models
- Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
- Loop Quantum Dynamics of the Schwarzschild Interior
- Are loop quantum cosmos never singular?
- Loop quantum cosmology and the k = - 1 RW model
- Closed FRW model in Loop Quantum Cosmology
- Anti-deSitter universe dynamics in LQC
- Loop cosmological dynamics and dualities with Randall-Sundrum braneworlds
- Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations
- Is loop quantization in cosmology unique?
- Phenomenological loop quantum geometry of the Schwarzschild black hole
- Loop Quantization of Vacuum Bianchi I Cosmology
- Lattice refining loop quantum cosmology, anisotropic models and stability
- Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I
- Loop Quantum Cosmology in Bianchi Type I Models: Analytical Investigation
- Positive cosmological constant in loop quantum cosmology
- The behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology
- Inhomogeneous Loop Quantum Cosmology: Hybrid Quantization of the Gowdy Model
- Cosmological footprints of loop quantum gravity
- Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology
- Quantum suppression of the generic chaotic behavior close to cosmological singularities
- Open FRW model in Loop Quantum Cosmology
- Prescriptions in Loop Quantum Cosmology: A comparative analysis
- Loop Quantum Cosmology of Diagonal Bianchi Type I model: simplifications and scaling problems
- Effective equations for isotropic quantum cosmology including matter
- Wave functions for the Schwarschild black hole interior
- Loop quantum cosmology with higher order holonomy corrections
- Numerical techniques for solving the quantum constraint equation of generic lattice-refined models in loop quantum cosmology
- Numerical solutions to lattice-refined models in loop quantum cosmology
- Unique factor ordering in the continuum limit of LQC
- Instabilities in numerical loop quantum cosmology
- Numerical Analysis of the Big Bounce in Loop Quantum Cosmology
- Unstable Anisotropic Loop Quantum Cosmology
Cited by in corpus (15)
- Quantum cosmology: a review
- Loop quantization of the Schwarzschild interior revisited
- Numerical simulations of a loop quantum cosmos: robustness of the quantum bounce and the validity of effective dynamics
- Numerical evolution of squeezed and non-Gaussian states in loop quantum cosmology
- Geodesic completeness and the lack of strong singularities in effective loop quantum Kantowski-Sachs spacetime
- Numerical loop quantum cosmology: an overview
- Von-Neumann Stability and Singularity Resolution in Loop Quantized Schwarzschild Black Hole
- Loop Quantum Cosmology: A brief review
- Glimpses of Space-Time Beyond the Singularities Using Supercomputers
- Implications of quantum ambiguities in k=1 loop quantum cosmology: distinct quantum turnarounds and the super-Planckian regime
- Von Neumann stability of modified loop quantum cosmologies
- Loop Quantum Cosmology
- Classical versus quantum evolution for a universe with a positive cosmological constant
- Cosmological dynamics in spin-foam loop quantum cosmology: challenges and prospects
- Basis Function Method for Numerical Loop Quantum Cosmology: The Schwarzschild Black Hole Interior