Natural inflation with multiple sub-Planckian axions

Abstract

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 ${f}_{\text{eff}}\ensuremath{\gg}{M}_{\mathrm{Pl}}$ through an alignment of the anomaly coefficients of multiple axions having sub-Planckian fundamental decay constants ${f}_{0}\ensuremath{\ll}{M}_{\mathrm{Pl}}$. The original version of the KNP mechanism realized with two axions requires that some of the anomaly coefficients should be of the order of ${f}_{\text{eff}}/{f}_{0}$, which would be uncomfortably large if ${f}_{\text{eff}}/{f}_{0}\ensuremath{\gtrsim}\mathcal{O}(100)$ as suggested by the recent BICEP2 results. We note that the KNP mechanism can be realized with the anomaly coefficients of $\mathcal{O}(1)$ if the number of axions $N$ is large as $N\mathrm{ln}N\ensuremath{\gtrsim}2\mathrm{ln}({f}_{\text{eff}}/{f}_{0})$, in which case the effective decay constant can be enhanced as ${f}_{\text{eff}}/{f}_{0}\ensuremath{\sim}\sqrt{N!}{n}^{N\ensuremath{-}1}$ 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 $N\ensuremath{\sim}{f}_{\text{eff}}^{2}/{f}_{0}^{2}$, 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 $\mathcal{O}({f}_{0}/{f}_{\text{eff}})$ under a random choice of the anomaly coefficients. We also present a simple model realizing a multiple axion monodromy along the inflaton direction.