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Nonlinear Extensions for the Inflationary Power Spectra

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We expound several principles in an attempt to clarify
the debate over infrared loop corrections to the primordial scalar and tensor
power spectra from inflation. Among other things we note that existing
proposals for nonlinear extensions of the scalar fluctuation field $\zeta$
introduce new ultraviolet divergences which no one understands how to
renormalize. Loop corrections and higher correlators of these putative
observables would also be enhanced by inverse powers of the slow roll parameter
$\epsilon$. We propose an extension which might be better behaved.