  We study models of inflation where the inflaton corresponds to a flat
direction in field space and its mass term is generated by gravity mediated
soft supersymmetry breaking at high scale. Assuming the inflaton to have non
negligible couplings to other fields, its mass runs with scale and can reach
the small value required by slow roll inflation at a lower scale, even if its
initial value is too large. Slow roll inflation can therefore take place in
such a regime, as long as the mass remains small, with a spectral index that is
then scale dependent. We explore the parameter space of this kind of models to
find the region compatible with the present observations.
