The coupling of topology and inflation in Noncommutative Cosmology

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 are 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.

30 pages, LaTeX, 11 pdf figures

References in corpus (4)

• Constraining the Noncommutative Spectral Action via Astrophysical Observations
• Supersymmetric QCD and noncommutative geometry
• The spectral action and cosmic topology
• Boundary conditions of the RGE flow in the noncommutative geometry approach to particle physics and cosmology

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• Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models
• Spectral Action Models of Gravity on Packed Swiss Cheese Cosmology
• A conceptual problem for non-commutative inflation and the new approach for non-relativistic inflationary equation of state
• Superradiance scattering of scalar, electromagnetic, and gravitational fields and thin accretion disk around non-commutating Kerr black hole
• Spectral action for a one-parameter family of Dirac-type operators on SU(2) and its inflation model
• Fractality in Cosmic Topology Models with Spectral Action Gravity