On almost commutative Friedmann-Lemaître-Robertson-Walker geometries

Abstract

We analyze the leading terms of the spectral action for a model of noncommutative geometry, which is a product of $4$-dimensional Riemannian manifold with a two-point space exploring the previously neglected case when the metrics over each sheet are different. Assuming the Friedmann-Lemaître-Robertson-Walker type of the metric for both sheets we obtain the action, which in addition to the the usual cosmological constant terms and the Einstein-Hilbert term involves a nonlinear interaction term. We study qualitative picture of potential consequences of such term in the basic cosmological models.

13 pages

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Cited by in corpus (5)

• On stability of Friedmann-Lemaître-Robertson-Walker solutions in doubled geometries
• Spectral interaction between universes
• Towards modified bimetric theories within non-product spectral geometry
• Spectral interactions between strings in the Higgs background
• A bigravity model from noncommutative geometry