Enhancement of the Axion Decay Constant in Inflation and the Weak Gravity Conjecture

Models of axion inflation based on a single cosine potential require the axion decay constant $f$ to be super-Planckian in size. However, $f > M_{Pl}$ is disfavored by the Weak Gravity Conjecture (WGC). It is then pertinent to ask if one can construct axion inflation models in conformity with WGC. In this work we assume that WGC holds for the microscopic Lagrangian so that $f < M_{Pl}$. However, inflation is controlled by an effective Lagrangian much below the Planck scale where the inflaton is an effective axionic field associated with an effective decay constant $f_e$ which could be very different from $f$. In this work we propose a Coherent Enhancement Mechanism (CEM) for slow roll inflation controlled by flat potentials which can produce $f_e \gg M_{Pl}$ while $f < M_{Pl}$. In the analysis we consider a landscape of chiral fields charged under a $U\left(1\right)$ global shift symmetry and consider breaking of the $U\left(1\right)$ symmetry by instanton type symmetry breaking terms. In the broken phase there is one light pseudo-Nambu-Goldstone-Boson (pNGB) which acts as the inflaton. We show that with an appropriate choice of symmetry breaking terms the inflaton potential is a superposition of many cosines and the condition that they produce a flat potential allows one to enhance $f_e$ so that $f_e / M_{Pl} \gg 1$. We discuss the utility of this mechanism for a variety of inflaton models originating in supersymmetry and supergravity. The Coherent Enhancement Mechanism allows one to reduce an inflation model with an arbitrary potential to an effective model of natural inflation, i.e. with a single cosine, by expanding the potential near a field point where horizon exit occurs, and matching the expansion coefficients to those of natural inflation.