Trajectories with suppressed tensor-to-scalar ratio in Aligned Natural Inflation

Abstract

In Aligned Natural Inflation, an alignment between different potential terms produces an inflaton excursion greater than the axion scales in the potential. We show that, starting from a general potential of two axions with two aligned potential terms, the effective theory for the resulting light direction is characterized by four parameters: an effective potential scale, an effective axion constant, and two extra parameters (related to ratios of the axion scales and the potential scales in the $2-$field theory). For all choices of these extra parameters, the model can support inflation along valleys (in the $2-$field space) that end in minima of the potential. This leads to a phenomenology similar to that of single field Natural Inflation. For a significant range of the extra two parameters, the model possesses also higher altitude inflationary trajectories passing through saddle points of the $2-$field potential, and disconnected from any minimum. These plateaus end when the heavier direction becomes unstable, and therefore all of inflation takes place close to the saddle point, where - due to the higher altitude - the potential is flatter (smaller $\epsilon$ parameter). As a consequence, a tensor-to-scalar ratio $r = {\rm O } \left( 10^{-4} - 10^{-2} \right)$ can be easily achieved in the allowed $n_s$ region, well within the latest $1 \sigma$ CMB contours.