Coupling of gravity to matter, spectral action and cosmic topology
- Creators
- Ćaćić, Branimir
- Marcolli, Matilde
- Teh, Kevin
Abstract
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.
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.Attached Files
Submitted - 1106.5473.pdf
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Additional details
- Eprint ID
- 51770
- DOI
- 10.4171/JNCG/162
- Resolver ID
- CaltechAUTHORS:20141114-110040989
- DMS-0901221
- NSF
- DMS-1007207
- NSF
- DMS-1201512
- NSF
- PHY-1205440
- NSF
- Created
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2014-11-14Created from EPrint's datestamp field
- Updated
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2021-11-10Created from EPrint's last_modified field