  Inflationary cosmology represents a well-studied framework to describe the
expansion of space in the early universe, as it explains the origin of the
large-scale structure of the cosmos and the isotropy of the cosmic microwave
background radiation. The recent detection of the Higgs boson renewed research
activities based on the assumption that the inflaton could be identified with
the Higgs field. At the same time, the question whether the inflationary
potential can be be extended to the electroweak scale and whether it should be
necessarily chosen ad hoc in order to be physically acceptable are at the
center of an intense debate. Here, we perform the slow-roll analysis of the
so-called Massive Natural Inflation (MNI) model which has three adjustable
parameters, the explicit mass term, a Fourier amplitude u, and a frequency
parameter $\beta$, in addition to a constant term of the potential. This theory
has the advantage to present a structure of infinite non-degenerate minima and
is amenable to an easy integration of high-energy modes. We show that, using
PLANCK data, one can fix, in the large $\beta$-region, the parameters of the
model in a unique way. We also demonstrate that the value for the parameters
chosen at the cosmological scale does not influence the results at the
electroweak scale. We argue that other models can have similar properties both
at cosmological and electroweak scales, but with the MNI model one can complete
the theory towards low energies and easily perform the integration of modes up
to the electroweak scale, producing the correct order-of-magnitude for the
Higgs mass.
