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:PrefaceAcknowledgmentsGravity and Matter in Noncommutative GeometryRenormalization Group Flows and Early Universe ModelsCosmic TopologyAlgebro-geometric Models in CosmologyMixmaster CosmologiesThe Spectral Action on Bianchi IX CosmologiesFractal and Multifractal Structures in CosmologyNoncommutative Quantum CosmologyBibliography
Readership: Graduate students and researchers in mathematical physics and theoretical cosmology.
Keywords:Cosmology;Gravity;Particle Physics;GeometryReview: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