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We propose a natural inflation model driven by an imaginary or axioniccomponent of a K\"ahler modulus in string-inspired supergravity. The shiftsymmetry of the axion is gauged under an anomalous $U(1)_X$ symmetry, whichleads to a modulus-dependent Fayet-Iliopoulos (FI) term. The matter fields arestabilized by F-terms, and the real component of the modulus is stabilized bythe $U(1)_X$ D-term, while its axion remains light. Therefore, the masses ofreal and imaginary components of the modulus are separated at different scales.The scalar potential for natural inflation is realized by the superpotentialfrom the non-perturbative effects. The trans-Planckian axion decay constant,which is needed to fit with BICEP2 observations, can be obtained naturally inthis model.

Natural Inflation with Natural Trans-Planckian Axion Decay Constant from Anomalous $U(1)_X$