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The Coupling of Topology and Inflation in Noncommutative Cosmology

Marcolli, Matilde and Pierpaoli, Elena and Teh, Kevin (2012) The Coupling of Topology and Inflation in Noncommutative Cosmology. Communications in Mathematical Physics, 309 (2). pp. 341-369. ISSN 0010-3616. http://resolver.caltech.edu/CaltechAUTHORS:20120203-142242831

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Abstract

We show that, in a model of modified gravity based on the spectral action functional, there is a nontrivial coupling between cosmic topology and inflation, in the sense that the shape of the possible slow-roll inflation potentials obtained in the model from the nonperturbative form of the spectral action is sensitive not only to the geometry (flat or positively curved) of the universe, but also to the different possible non-simply connected topologies. We show this by explicitly computing the nonperturbative spectral action for some candidate flat cosmic topologies given by Bieberbach manifolds and showing that the resulting inflation potential differs from that of the flat torus by a multiplicative factor, similarly to what happens in the case of the spectral action of the spherical forms in relation to the case of the 3-sphere. We then show that, while the slow-roll parameters differ between the spherical and flat manifolds but do not distinguish different topologies within each class, the power spectra detect the different scalings of the slow-roll potential and therefore distinguish between the various topologies, both in the spherical and in the flat case.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s00220-011-1352-4DOIArticle
http://www.springerlink.com/content/ur3288jj826000wx/PublisherArticle
https://arxiv.org/abs/1012.0780arXivDiscussion Paper
Additional Information:© 2011 Springer-Verlag. Received: 9 December 2010. Accepted: 26 April 2011. Published online: 4 October 2011. Communicated by A. Connes.
Group:TAPIR
Record Number:CaltechAUTHORS:20120203-142242831
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120203-142242831
Official Citation:The Coupling of Topology and Inflation in Noncommutative Cosmology Matilde Marcolli, Elena Pierpaoli and Kevin Teh pp.341-369
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29131
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:03 Feb 2012 22:39
Last Modified:12 Jul 2017 23:09

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