Cosmological Coleman-Weinberg potentials and inflation

We consider an additional fine-tuning problem which afflicts scalar-driven models of inflation. The problem is that successful reheating requires the inflaton be coupled to ordinary matter, and quantum fluctuations of this matter induce Coleman-Weinberg potentials which are not Planck suppressed. Unlike the flat space case, these potentials depend upon a still-unknown, nonlocal functional of the metric which reduces to the Hubble parameter for de Sitter. Such a potential cannot be completely subtracted off by any local action. In a simple model we numerically consider one possible subtraction scheme in which the correction is locally subtracted at the beginning of inflation. For fermions the effect is to make the Universe approach de Sitter with a smaller Hubble parameter. For gauge bosons the effect is to make inflation end almost instantly unless the gauge charge is unacceptably small.