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Coupling of gravity to matter, spectral action and cosmic topology

Ćaćić, Branimir and Marcolli, Matilde and Teh, Kevin (2014) Coupling of gravity to matter, spectral action and cosmic topology. Journal of Noncommutative Geometry, 8 (2). pp. 473-504. ISSN 1661-6952. doi:10.4171/JNCG/162.

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We consider a model of modified gravity based on the spectral action functional, for a cosmic topology given by a spherical space form, and the associated slow-roll inflation scenario. We consider then the coupling of gravity to matter determined by an almost-commutative geometry over the spherical space form. We show that this produces a multiplicative shift of the amplitude of the power spectra for the density fluctuations and the gravitational waves, by a multiplicative factor equal to the total number of fermions in the matter sector of the model. We obtain the result by an explicit nonperturbative computation, based on the Poisson summation formula and the spectra of twisted Dirac operators on spherical space forms, as well as, for more general spacetime manifolds, using a heat kernel computation.

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Additional Information:© 2014 European Mathematical Society. Received December 15, 2011; revised June 26, 2012. This work is partially supported by NSF grants DMS-0901221, DMS-1007207, DMS-1201512, PHY-1205440. The second author thanks José Luis Cisneros-Molina for a useful conversation and for pointing out to us the results of [9], and the first author thanks Mathai Varghese for useful conversations.
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Subject Keywords:Spectral action, cosmic topology, gravity coupled to matter, Poisson summation formula, heat kernel
Issue or Number:2
Classification Code:MSC 2010: 83F05, 83C65, 58J42
Record Number:CaltechAUTHORS:20141114-110040989
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51770
Deposited By: Ruth Sustaita
Deposited On:14 Nov 2014 22:03
Last Modified:10 Nov 2021 19:15

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