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 f eff ≫ M Pl through an alignment of the anomaly coefficients of multiple axions having sub-Planckian fundamental decay constants f 0 ≪ M Pl . The original version of the KNP mechanism realized with two axions requires that some of the anomaly coefficients should be of the order of f eff / f 0 , which would be uncomfortably large if f eff / f 0 ≳ O ( 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 N ln N ≳ 2 ln ( f eff / f 0 ) , in which case the effective decay constant can be enhanced as f eff / f 0 ∼ 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 ∼ f eff 2 / f 0 2 , 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 ( f 0 / f eff ) under a random choice of the anomaly coefficients. We also present a simple model realizing a multiple axion monodromy along the inflaton direction.