Journal article 321 views
Bell Polynomials and Brownian Bridge in Spectral Gravity Models on Multifractal Robertson–Walker Cosmologies
Annales Henri Poincaré, Volume: 21, Issue: 4, Pages: 1329 - 1382
Swansea University Author: Farzad Fathi Zadeh
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DOI (Published version): 10.1007/s00023-020-00894-5
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...
| Published in: | Annales Henri Poincaré |
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| ISSN: | 1424-0637 1424-0661 |
| Published: |
Springer Science and Business Media LLC
2020
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa55855 |
| 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–Walkerspacetime, 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 fromthe poles (off the real line) of this zeta function. |
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| Keywords: |
Robertson-Walker metrics, Dirac Laplacian, Heat kernel expansion, Feynman-Kac formula, Brownian bridge |
| College: |
Faculty of Science and Engineering |
| Issue: |
4 |
| Start Page: |
1329 |
| End Page: |
1382 |