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SIGMA, 2012, Volume 8, 001, 26 pages (Mi sigma678)  

This article is cited in 20 scientific papers (total in 20 papers)

Numerical techniques in loop quantum cosmology

David Brizuelaa, Daniel Cartinb, Gaurav Khannac

a Institute for Gravitation and the Cosmos, The Pennsylvania State University, 104 Davey Lab, University Park, Pennsylvania 16802, USA
b Naval Academy Preparatory School, 197 Elliot Avenue, Newport, Rhode Island 02841, USA
c Physics Department, University of Massachusetts at Dartmouth, North Dartmouth, Massachusetts 02747, USA

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.

Keywords: quantum gravity, numerical techniques, loop quantum cosmology.


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ArXiv: 1110.0646
MSC: 83C45; 83Fxx; 83-08
Received: October 1, 2011; in final form December 20, 2011; Published online January 2, 2012

Citation: David Brizuela, Daniel Cartin, Gaurav Khanna, “Numerical techniques in loop quantum cosmology”, SIGMA, 8 (2012), 001, 26 pp.

Citation in format AMSBIB
\by David Brizuela, Daniel Cartin, Gaurav Khanna
\paper Numerical techniques in loop quantum cosmology
\jour SIGMA
\yr 2012
\vol 8
\papernumber 001
\totalpages 26

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    This publication is cited in the following articles:
    1. P. Singh, “Numerical loop quantum cosmology: an overview”, Class. Quantum Gravity, 29:24 (2012), 244002  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. D. Cartin, “Conserved quantities in isotropic loop quantum cosmology”, EPL, 98:3 (2012), 30007  crossref  adsnasa  isi  scopus
    3. B. Gupt, P. Singh, “A quantum gravitational inflationary scenario in Bianchi-I spacetime”, Class. Quantum Gravity, 30:14 (2013), 145013  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. P. Diener, B. Gupt, P. Singh, “Chimera: a hybrid approach to numerical loop quantum cosmology”, Class. Quantum Gravity, 31:2 (2014), 025013  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. P. Diener, B. Gupt, P. Singh, “Numerical simulations of a loop quantum cosmos: robustness of the quantum bounce and the validity of effective dynamics”, Class. Quantum Gravity, 31:10 (2014), 105015  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. P. Diener, B. Gupt, M. Megevand, P. Singh, “Numerical evolution of squeezed and non-Gaussian states in loop quantum cosmology”, Class. Quantum Gravity, 31:16 (2014), 165006  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. I. Agullo, A. Corichi, “Loop quantum cosmology”, Springer Handbook of Spacetime, 2014, 809–839  crossref  mathscinet  isi  scopus
    8. Singh P., “Loop Quantum Cosmology and the Fate of Cosmological Singularities”, Bull. Astron. Soc. India., 42:3-4 (2014), 121–146  isi
    9. D. Brizuela, “Classical versus quantum evolution for a universe with a positive cosmological constant”, Phys. Rev. D, 91:8 (2015), 085003  crossref  mathscinet  adsnasa  isi  elib  scopus
    10. M. Bojowald, “Quantum cosmology: a review”, Rep. Prog. Phys., 78:2 (2015), 023901  crossref  mathscinet  adsnasa  isi  elib  scopus
    11. S. Saini, P. Singh, “Geodesic completeness and the lack of strong singularities in effective loop quantum Kantowski–Sachs spacetime”, Class. Quantum Gravity, 33:24 (2016), 245019  crossref  mathscinet  zmath  isi  scopus
    12. Ch. C. Dantas, “An inhomogeneous space-time patching model based on a nonlocal and nonlinear Schrödinger equation”, Found. Phys., 46:10 (2016), 1269–1292  crossref  mathscinet  zmath  isi  elib  scopus
    13. P. Singh, “Is classical flat Kasner spacetime flat in quantum gravity?”, Int. J. Mod. Phys. D, 25:8, SI (2016), 1642001  crossref  mathscinet  zmath  isi  elib  scopus
    14. Corichi A., Singh P., “Loop Quantization of the Schwarzschild Interior Revisited”, Class. Quantum Gravity, 33:5 (2016), 055006  crossref  mathscinet  zmath  isi  scopus
    15. P. Diener, A. Joe, M. Megevand, P. Singh, “Numerical simulations of loop quantum Bianchi-I spacetimes”, Class. Quantum Gravity, 34:9 (2017), 094004  crossref  zmath  isi  scopus
    16. D. A. Craig, P. Singh, “Cosmological dynamics in spin-foam loop quantum cosmology: challenges and prospects”, Class. Quantum Gravity, 34:7 (2017), 074001  crossref  mathscinet  zmath  isi  scopus
    17. J. L. Dupuy, P. Singh, “Implications of quantum ambiguities in $k=1$ loop quantum cosmology: distinct quantum turnarounds and the super-Planckian regime”, Phys. Rev. D, 95:2 (2017), 023510  crossref  isi  scopus
    18. A. Yonika, G. Khanna, P. Singh, “von-Neumann stability and singularity resolution in loop quantized Schwarzschild black hole”, Class. Quantum Gravity, 35:4 (2018), 045007  crossref  mathscinet  zmath  isi  scopus
    19. P. Singh, “Glimpses of space-time beyond the singularities using supercomputers”, Comput. Sci. Eng., 20:4 (2018), 26–38  crossref  isi  scopus
    20. Saini S., Singh P., “Von Neumann Stability of Modified Loop Quantum Cosmologies”, Class. Quantum Gravity, 36:10 (2019), 105010  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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