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This course covers the cosmological consequences of the spectral principle in almost commutative manifolds, including the constraints on cutoff momenta using astrophysical data and the role of scalar fields. It also discusses an alternative definition of the bosonic spectral action based on zeta function regularization. The teaching method involves a lecture within a specific mathematical framework. The course is intended for individuals interested in noncommutative spectral geometry and its applications in cosmology and theoretical physics.
