  We analyze quantum corrections on the naive $\phi^4$-Inflation. These
typically lead to an inflaton potential which carries a non-integer power of
the field. We consider both minimal and non-minimal couplings to gravity. For
the latter case we also study unitarity of inflaton-inflaton scattering.
Finally we confront these theories with the Planck and BICEP2 data. We
demonstrate that the discovery of primordial tensor modes by BICEP2 require the
presence of sizable quantum departures from the $\phi^4$-Inflaton model for the
non-minimally coupled scenario which we parametrize and quantify. We compare
the results with the minimally coupled case and elucidate the main distinctive
features.
