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.
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