  Adopting a recently proposed single-superfield framework of supergravity
inflation, we consider large field inflationary models in which MSSM Higgs-like
fields play the role of the inflaton. In the simplest cases, the inflaton
potential has a fractional power, which is different from that of the original
Higgs inflation, and it can be tested by cosmological observations in near
future. We find difficulties in identifying the inflaton with the MSSM Higgses
and discuss possible candidates of the inflaton.
