Non-canonical inflation in supergravity

We investigate the effect of non-canonical kinetic terms on inflation in supergravity. We find that the biggest impact of such higher-derivative kinetic terms is due to the corrections to the potential that they induce via their effect on the auxiliary fields, which now have a cubic equation of motion. This is in contrast to the usual (non-supersymmetric) effective field theory expansion which assumes that mass-suppressed higher-derivative terms do not affect the lower-derivative terms already present. We demonstrate with several examples that such changes in the potential can significantly modify the inflationary dynamics. Our results have immediate implications for effective descriptions of inflation derived from string theory, where higher-derivative kinetic terms are generally present. In addition we elucidate the structure of the theory in the parameter range where there are three real solutions to the auxiliary field's equation of motion, studying the resulting three branches of the theory, and finding that one of them suffers from a singularity in the speed of propagation of fluctuations.