A detection of primordial tensor modes could be explained in terms of a model of large-field high-scale inflation. Theoretical considerations suggest that a symmetry should be invoked in order to protect the flatness of the inflaton potential and hence an axion enjoying a shift symmetry is a natural candidate. I review the construction and the remarkable phenomenological consequences of this class of models, pointing out that there is series of observables that correlate with large primordial tensor modes: oscillations in all N-point functions, large primordial gravity waves at interferometers, blue running of the spectral index and non-Gaussianity. In the second part of the talk I switch gear and discuss spectral distortion of the CMB. mu-type distortion provides a unique probe of primordial perturbations at scales as small as a kpc (!), which are so far completely unconstrained. I show that cross correlations of mu-type distortion with temperature anisotropies are a direct probe of the primordial bispectrum in a much more squeezed limit than what can be probed using just temperature anisotropies or large scale structures. With current technologies one could already achieve a sensitivity of \Delta f_NL~1000. As experiments get better, this bound can be improved almost arbitrarily due to the practical absence of the cosmic variance of mu-distortion.