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.
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