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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. doi:10.1007/s00220-011-1352-4.

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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.

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Pierpaoli, Elena0000-0002-7957-8993
Additional Information:© 2011 Springer-Verlag. Received: 9 December 2010. Accepted: 26 April 2011. Published online: 4 October 2011. Communicated by A. Connes.
Issue or Number:2
Record Number:CaltechAUTHORS:20120203-142242831
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Official Citation:Marcolli, M., Pierpaoli, E. & Teh, K. The Coupling of Topology and Inflation in Noncommutative Cosmology. Commun. Math. Phys. 309, 341–369 (2012).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29131
Deposited By: Ruth Sustaita
Deposited On:03 Feb 2012 22:39
Last Modified:09 Nov 2021 17:04

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