The spectral action and cosmic topology

Details The spectral action and cosmic topology The spectral action and cosmic topology

2010-05-13

arxiv.org/abs/1005.2256v1

Commun.Math.Phys.304:125-174,2011

Physics

High Energy Physics

High Energy Physics - Theory

55 pages, LaTeX

Scientific paper

10.1007/s00220-011-1211-3

The spectral action functional, considered as a model of gravity coupled to matter, provides, in its non-perturbative form, a slow-roll potential for inflation, whose form and corresponding slow-roll parameters can be sensitive to the underlying cosmic topology. We explicitly compute the non-perturbative spectral action for some of the main candidates for cosmic topologies, namely the quaternionic space, the Poincare' dodecahedral space, and the flat tori. We compute the corresponding slow-roll parameters and see we check that the resulting inflation model behaves in the same way as for a simply-connected spherical topology in the case of the quaternionic space and the Poincare' homology sphere, while it behaves differently in the case of the flat tori. We add an appendix with a discussion of the case of lens spaces.

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