Early universe models from noncommutative geometry. (English) Zbl 1243.83005

Marcolli, Matilde; Pierpaoli, Elena

Adv. Theor. Math. Phys. 14, No. 5, 1373-1432 (2010).

Summary: We investigate cosmological predictions on the early universe based on the noncommutative geometry (NCG) models of gravity coupled to matter. Using the renormalization group analysis for the standard model with right-handed neutrinos and Majorana mass terms, which is the particle physics content of the most recent NCG models, we analyze the behavior of the coefficients of the gravitational and cosmological terms in the Lagrangian derived from the asymptotic expansion of the spectral action functional of NCG. We find emergent Hoyle-Narlikar and conformal gravity at the see-saw scales and a running effective gravitational constant, which affects the propagation of gravitational waves and the evaporation law of primordial black holes and provides Linde models of negative gravity in the early universe. The same renormalization group analysis also governs the running of the effective cosmological constant of the model. The model also provides a Higgs-based slow-roll inflationary mechanism, for which one can explicitly compute the slow-roll parameters. The particle physics content allows for dark matter models based on sterile neutrinos with Majorana mass terms.

MSC:

83-02	Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83C65	Methods of noncommutative geometry in general relativity
83F05	Relativistic cosmology
81T17	Renormalization group methods applied to problems in quantum field theory
83C35	Gravitational waves
83D05	Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
85A40	Astrophysical cosmology
83C57	Black holes

Software:

REAP

References:

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