Evidence for Inflation in an Axion Landscape

We discuss inflation models within supersymmetry and supergravity frameworks with a landscape of chiral superfields and one $U(1)$ shift symmetry which is broken by non-perturbative symmetry breaking terms in the superpotential. We label the pseudo scalar component of the chiral fields axions and their real parts saxions. Thus in the models only one combination of axions will be a pseudo-Nambu-Goldstone-boson which will act as the inflaton. The proposed models constitute consistent inflation for the following reasons: The inflation potential arises dynamically with stabilized saxions, the axion decay constant can lie in the sub-Planckian region, and consistency with the Planck data is achieved. The axion landscape consisting of $m$ axion pairs is assumed with the axions in each pair having opposite charges. A fast roll--slow roll splitting mechanism for the axion potential is proposed which is realized with a special choice of the axion basis. In this basis the $2m$ coupled equations split into $2m-1$ equations which enter in the fast roll and there is one unique linear combination of the $2m$ fields which controls the slow roll and thus the power spectrum of curvature and tensor perturbations. It is shown that a significant part of the parameter space exists where inflation is successful, i.e., $N_{\rm pivot} = {[50, 60]}$, the spectral index $n_s$ of curvature perturbations, and the ratio $r$ of the power spectrum of tensor perturbations and curvature perturbations, lie in the experimentally allowed regions given by the Planck experiment. Further, it is shown that the model allows for a significant region of the parameter space where the effective axion decay constant can lie in the sub-Planckian domain.