Natural and multi-natural inflation in axion landscape

We propose a landscape of many axions, where the axion potential receives various contributions from shift symmetry breaking effects. We show that the existence of the axion with a super-Planckian decay constant is very common in the axion landscape for a wide range of numbers of axions and shift symmetry breaking terms, because of the accidental alignment of axions. The effective inflation model is either natural or multi-natural inflation in the axion landscape, depending on the number of axions and the shift symmetry breaking terms. The tension between BICEP2 and Planck could be due to small modulations to the inflaton potential or steepening of the potential along the heavy axions after the tunneling. The total duration of the slow-roll inflation our universe experienced is not significantly larger than 60 if the typical height of the axion potentials is of order (10 16−17 GeV) 4