Aspects of the Bosonic Spectral Action: Successes and Challenges
  A short introduction on elements of noncommutative geometry, which offers a
purely geometric interpretation of the Standard Model and implies a higher
derivative gravitational theory, is presented. Physical consequences of almost
commutative manifolds are briefly discussed and cosmological consequences of
the gravitational sector, which is shown not to be plagued by linear
instability, are highlighted. Successes and challenges are discussed. A novel
spectral action proposal based on zeta function regularisation is briefly
presented.
