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Integrating out Heavy Fields in Inflation

I present the procedure for integrating out quantum fields whose mass M is well above the Hubble scale H in de Sitter space. The effective interaction and density matrix are explicitly computed for a simple example and are found to be of order H/M, are nonlocally distributed in time and contain a highly oscillatory phase. This radical departure from the static space-time result demonstrates that these new tools are necessary for constructing effective inflationary potentials. The effective coupling naturally forms a perturbative series in the relative energy transferred ΔE/M, whose coefficients can then be compared to observation.