General analysis of inflation in the Jordan frame supergravity

We study various inflation models in the Jordan frame supergravity with a logarithmic K̈ahler potential. We find that, in a class of inflation models containing an additional singlet in the superpotential, three types of chaotic inflation can be realized: the Higgs-type inflation, power-law inflation, and inflation with/without a running kinetic term. The former two are possible if the holomorphic function dominates over the non-holomorphic one in the frame function, while the inflation with/without a running kinetic term occurs when both are comparable. Interestingly, the fractional-power potential can be realized by the running kinetic term. We also discuss the implication for the Higgs inflation in supergravity.