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In string theory compactifications it is common to find an effectiveLagrangian for the scalar fields with a non-canonical kinetic term. We studythe effective action of the scalar position moduli of Type II D$p$-branes. Inmany instances the kinetic terms are in fact modified by a term proportional tothe scalar potential itself. This can be linked to the appearance ofhigher-dimensional supersymmetric operators correcting the K\"ahler potential.We identify the supersymmetric dimension-eight operators describing the$\alpha'$ corrections captured by the D-brane Dirac-Born-Infeld action. Ouranalysis then allows an embedding of the D-brane moduli effective action intoan $\mathcal N = 1$ supergravity formulation. The effects of thepotential-dependent kinetic terms may be very important if one of the scalarsis the inflaton, since they lead to a flattening of the scalar potential. Weanalyze this flattening effect in detail and compute its impact on the CMBobservables for single-field inflation with monomial potentials.

The DBI Action, Higher-derivative Supergravity, and Flattening Inflaton Potentials