Bounds for the scale of inflation and the tensor-to-scalar ratio in
  Hybrid Natural Inflation
  Recently we have studied in great detail a model of Hybrid Natural Inflation
(HNI) by constructing two simple effective field theories. These two versions
of the model allow inflationary energy scales as small as the electroweak scale
in one of them or as large as the Grand Unification scale in the other
therefore covering the whole range of possible energy scales. The inflationary
sector of the model is of the form $V(\phi)=V_0 \left(1+a \cos(\phi/f)\right)$
where $0\leq a<1$ and the end of inflation is triggered by an independent
waterfall field. One interesting characteristic of this type of models is that
the tensor-to-scalar ratio $r$ is a non-monotonic function of $\phi$ presenting
a {\it maximum} close to the inflection point $\phi_I=\pi/2$ of the potential.
Because the scalar spectrum $\mathcal{P}_s(k)$ of density fluctuations when
written in terms of the potential is inversely proportional to $r$ we find that
$\mathcal{P}_s(k)$ presents a {\it minimum} at $\phi_{min}$. We use this
property of HNI together with the observation that the spectrum is decreasing
during the first 8 e-folds of observable inflation to determine bounds for the
inflationary energy scale $\Delta$ and for the tensor-to-scalar ratio $r$.
