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Spectral action for Bianchi type-IX cosmological models / Wentao Fan; Farzad Fathizadeh; Matilde Marcolli; Farzad Fathi Zadeh

Journal of High Energy Physics, Volume: 2015, Issue: 10

Swansea University Author: Farzad, Fathi Zadeh

Abstract

In this paper we prove a rationality phenomena for the coefficients of the heat kernel expansion of the Dirac-Laplacian of Bianchi IX cosmological models. Due the complexities arising from the anisotropic nature of the model, we present a novel method of writing the heat coefficients as Wodzicki res...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: 2015
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa40251
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Abstract: In this paper we prove a rationality phenomena for the coefficients of the heat kernel expansion of the Dirac-Laplacian of Bianchi IX cosmological models. Due the complexities arising from the anisotropic nature of the model, we present a novel method of writing the heat coefficients as Wodzicki resiudes of certain Laplacians and then provide an elegant proof of the rationality result. That is, we show that each coefficient is described by a several variable polynomial with rational coefficients of the cosmic expansion factors and their higher derivatives of a certain order. This result confirms the arithmetic nature of the complicated terms in the expansion.
Keywords: Bianchi IX model, Dirac operator, heat kernel expansion, pseudodifferential calculus, rationality, arithmetic structure
College: College of Science
Issue: 10