  Starting from a theory of fermions moving in a fixed gauge and gravitational
background we implement the scale invariance of the theory. Upon quantization
the theory is anomalous but the anomaly can be cancelled by the addition of
another term to the action. This term comes out to be basically the Chamseddine
Connes spectral action introduced in the context of noncommutative geometry. An
alternative realization of the dilaton may involve a collective scalar mode of
all fermions accumulated in a {scale-noninvariant} dilaton action. The entire
spectral action describes gauge and Higgs fields coupled with gravity. Here
this action is coupled with a dilaton and we discuss how it relates to the
transition from the radiation to the electroweak broken phase via condensation
of Higgs fields.
