Noncommutative Cosmology

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.

Contents:

• Preface
• Acknowledgments
• Gravity and Matter in Noncommutative Geometry
• Renormalization Group Flows and Early Universe Models
• Cosmic Topology
• Algebro-geometric Models in Cosmology
• Mixmaster Cosmologies
• The Spectral Action on Bianchi IX Cosmologies
• Motives and Periods in Cosmology
• Fractal and Multifractal Structures in Cosmology
• Noncommutative Quantum Cosmology
• Bibliography
• Index

Readership: Graduate students and researchers in mathematical physics and theoretical cosmology.
Key Features:

• 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