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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

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DOI (Published version): 10.1007/JHEP10(2015)085

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
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URI: https://cronfa.swan.ac.uk/Record/cronfa40251
first_indexed 2018-05-17T19:03:21Z
last_indexed 2019-08-16T15:02:52Z
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spelling 2019-08-16T10:50:17.7172187 v2 40251 2018-05-17 Spectral action for Bianchi type-IX cosmological models c1859f5040a279bcd3fa991d8f6e7f21 Farzad Fathi Zadeh Farzad Fathi Zadeh true false 2018-05-17 MACS 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. Journal Article Journal of High Energy Physics 2015 10 1029-8479 Bianchi IX model, Dirac operator, heat kernel expansion, pseudodifferential calculus, rationality, arithmetic structure 13 10 2015 2015-10-13 10.1007/JHEP10(2015)085 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2019-08-16T10:50:17.7172187 2018-05-17T17:07:16.0801675 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Wentao Fan 1 Farzad Fathizadeh 2 Matilde Marcolli 3 Farzad Fathi Zadeh 4 0040251-06082018151525.pdf Fan-2015-Spectral-action-for-bianchi-type-ix.pdf 2018-08-06T15:15:25.8630000 Output 659058 application/pdf Version of Record true 2018-08-06T00:00:00.0000000 true eng
title Spectral action for Bianchi type-IX cosmological models
spellingShingle Spectral action for Bianchi type-IX cosmological models
Farzad Fathi Zadeh
title_short Spectral action for Bianchi type-IX cosmological models
title_full Spectral action for Bianchi type-IX cosmological models
title_fullStr Spectral action for Bianchi type-IX cosmological models
title_full_unstemmed Spectral action for Bianchi type-IX cosmological models
title_sort Spectral action for Bianchi type-IX cosmological models
author_id_str_mv c1859f5040a279bcd3fa991d8f6e7f21
author_id_fullname_str_mv c1859f5040a279bcd3fa991d8f6e7f21_***_Farzad Fathi Zadeh
author Farzad Fathi Zadeh
author2 Wentao Fan
Farzad Fathizadeh
Matilde Marcolli
Farzad Fathi Zadeh
format Journal article
container_title Journal of High Energy Physics
container_volume 2015
container_issue 10
publishDate 2015
institution Swansea University
issn 1029-8479
doi_str_mv 10.1007/JHEP10(2015)085
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
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description 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.
published_date 2015-10-13T13:35:15Z
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