  Noncommutative spectral geometry succeeds in explaining the physics of the
Standard Model of electroweak and strong interactions in all its details as
determined by experimental data. Moreover, by construction the theory lives at
very high energy scales, offering a natural framework to address early universe
cosmological issues. After introducing the main elements of noncommutative
spectral geometry, I will summarise some of its cosmological consequences and
discuss constraints on the gravitational sector of the theory.
