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 induces 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 agrees with the Hubble parameter for de Sitter. Such a potential cannot be completely subtracted off by any local action. We numerically consider the effect of subtracting it off at the beginning of inflation in a simple model. For fermions the effect is to prevent inflation from ending unless the Yukawa coupling to the inflaton is so small as to endanger reheating. For gauge bosons the effect is to make inflation end almost instantly, again unless the gauge charge is unacceptably small.