Markov chain Monte Carlo methods for graph refinement in spinfoam cosmology

• Verfasst von: Frisoni, Pietropaolo [VerfasserIn]
• Verfasst von: Gozzini, Francesco [VerfasserIn]
• Verfasst von: Vidotto, Francesca [VerfasserIn]
• Titel: Markov chain Monte Carlo methods for graph refinement in spinfoam cosmology
• Verf.angabe: Pietropaolo Frisoni, Francesco Gozzini and Francesca Vidotto
• E-Jahr: 2023
• Jahr: 14 April 2023
• Umfang: 32 S.
• Illustrationen: Illustrationen
• Fussnoten: Gesehen am 21.09.2023
• Titel Quelle: Enthalten in: Classical and quantum gravity
• Ort Quelle: Bristol : IOP Publ., 1984
• Jahr Quelle: 2023
• Band/Heft Quelle: 40(2023), 10, Artikel-ID 105001, Seite 1-32
• ISSN Quelle: 1361-6382
• DOI: doi:10.1088/1361-6382/acc5d6
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 186014425X

Abstract

We study the behavior of the Lorentzian Engle-Pereira-Rovelli-Livine spinfoam amplitude with homogeneous boundary data, under a graph refinement going from five to twenty boundary tetrahedra. This can be interpreted as a wave function of the Universe, for which we compute boundary geometrical operators, correlation functions, and entanglement entropy. The numerical calculation is made possible by adapting the Metropolis-Hastings algorithm, along with recently developed computational methods appropriate for the deep quantum regime. We confirm that the transition amplitudes are stable against such refinement. We find that the average boundary geometry does not change, but the new degrees of freedom correct the quantum fluctuations of the boundary and the correlations between spatial patches. The expectation values are compatible with their geometrical interpretation and the correlations between neighboring patches decay when computed across different spinfoam vertices.