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Modified gravity models play an important role in contemporary theoretical cosmology. The present book proposes a novel approach to the topic based on techniques from noncommutative geometry, especially the spectral action functional as a gravity model. The book discusses applications to early universe models and slow-roll inflation models, to the problem of cosmic topology, to non-isotropic cosmologies like mixmaster universes and Bianchi IX gravitational instantons, and to multifractal structures in cosmology.
Relations between noncommutative and algebro-geometric methods in cosmology is also discussed, including the occurrence of motives, periods, and modular forms in spectral models of gravity.
Gravity and Matter in Noncommutative Geometry
Renormalization Group Flows and Early Universe Models
Algebro-geometric Models in Cosmology
The Spectral Action on Bianchi IX Cosmologies
Motives and Periods in Cosmology
Fractal and Multifractal Structures in Cosmology
Noncommutative Quantum Cosmology
Readership: Graduate students and researchers in mathematical physics and theoretical cosmology.
While there are recent books that focus on applications of noncommutative geometry to particle physics models, there is presently no other book that focuses on applications to cosmology