Natural inflation with multiple sub-Planckian axions

We extend the Kim-Nilles-Peloso (KNP) alignment mechanism for natural inflation to models with $N>2$ axions, which obtains super-Planckian effective axion decay constant feffMPl through an alignment of the anomaly coefficients of multiple axions having sub-Planckian fundamental decay constants f₀MPl. The original version of the KNP mechanism realized with two axions requires that some of the anomaly coefficients should be of the order of feff/f₀, which would be uncomfortably large if feff/f₀O(100) as suggested by the recent BICEP2 results. We note that the KNP mechanism can be realized with the anomaly coefficients of O(1) if the number of axions N is large as NlnN2ln(feff/f₀), in which case the effective decay constant can be enhanced as feff/f₀~√N!n^N-1 for n denoting the typical size of the integer-valued anomaly coefficients. Comparing to the other multiple axion scenario, the N-flation scenario which requires N~feff²/f₀², the KNP mechanism has a virtue of not invoking to a too large number of axions, although it requires a specific alignment of the anomaly coefficients, which can be achieved with a probability of O(f₀/feff) under a random choice of the anomaly coefficients. We also present a simple model realizing a multiple axion monodromy along the inflaton direction.