  In this paper we propose a novel definition of the bosonic spectral action
using zeta function regularization, in order to address the issues of
renormalizability and spectral dimensions. We compare the zeta spectral action
with the usual (cutoff based) spectral action and discuss its origin,
predictive power, stressing the importance of the issue of the three
dimensionful fundamental constants, namely the cosmological constant, the Higgs
vacuum expectation value, and the gravitational constant. We emphasize the
fundamental role of the neutrino Majorana mass term for the structure of the
bosonic action.
