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Bell Polynomials and Brownian Bridge in Spectral Gravity Models on Multifractal Robertson–Walker Cosmologies

Fathizadeh, Farzad and Kafkoulis, Yeorgia and Marcolli, Matilde (2020) Bell Polynomials and Brownian Bridge in Spectral Gravity Models on Multifractal Robertson–Walker Cosmologies. Annales Henri Poincaré, 21 (4). pp. 1329-1382. ISSN 1424-0637. https://resolver.caltech.edu/CaltechAUTHORS:20200211-084519645

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Abstract

We obtain an explicit formula for the full expansion of the spectral action on Robertson–Walker spacetimes, expressed in terms of Bell polynomials, using Brownian bridge integrals and the Feynman–Kac formula. We then apply this result to the case of multifractal Packed Swiss Cheese Cosmology models obtained from an arrangement of Robertson–Walker spacetimes along an Apollonian sphere packing. Using Mellin transforms, we show that the asymptotic expansion of the spectral action contains the same terms as in the case of a single Robertson–Walker spacetime, but with zeta-regularized coefficients, given by values at integers of the zeta function of the fractal string of the radii of the sphere packing, as well as additional log-periodic correction terms arising from the poles (off the real line) of this zeta function.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/s00023-020-00894-5DOIArticle
https://arxiv.org/abs/1811.02972arXivDiscussion Paper
ORCID:
AuthorORCID
Fathizadeh, Farzad0000-0002-7863-4009
Additional Information:© 2020 Springer Nature Switzerland AG. First Online: 10 February 2020. The first author acknowledges the support from the Marie Curie/SER Cymru II Cofund Research Fellowship 663830-SU-008 and thanks the Perimeter Institute for Theoretical Physics for their hospitality in July 2018 and their excellent environment where this work was partially carried out. The second author was partially supported by a Gantvoort Scholarship, a Mr. and Mrs. Robert C. Loschke Summer Undergraduate Research Fellowship, and a Taussky-Todd Prize. The third author was partially supported by NSF Grant DMS-1707882, by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement Grant RGPAS-2018-522593, and by the Perimeter Institute for Theoretical Physics.
Funders:
Funding AgencyGrant Number
Marie Curie Fellowship663830-SU-008
Gantvoort ScholarshipUNSPECIFIED
Caltech Summer Undergraduate Research Fellowship (SURF)UNSPECIFIED
Taussky-Todd PrizeUNSPECIFIED
NSFDMS-1707882
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPIN-2018-04937
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPAS-2018-522593
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:20200211-084519645
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200211-084519645
Official Citation:Fathizadeh, F., Kafkoulis, Y. & Marcolli, M. Bell Polynomials and Brownian Bridge in Spectral Gravity Models on Multifractal Robertson–Walker Cosmologies. Ann. Henri Poincaré 21, 1329–1382 (2020). https://doi.org/10.1007/s00023-020-00894-5
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101220
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:11 Feb 2020 16:59
Last Modified:25 Mar 2020 15:32

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