On the non-linear scale of cosmological perturbation theory
  We discuss the convergence of cosmological perturbation theory. We prove that
the polynomial enhancement of the non-linear corrections expected from the
effects of soft modes is absent in equal-time correlators like the power or
bispectrum. We first show this at leading order by resumming the most important
corrections of soft modes to an arbitrary skeleton of hard fluctuations. We
derive the same result in the eikonal approximation, which also allows us to
show the absence of enhancement at any order. We complement the proof by an
explicit calculation of the power spectrum at two-loop order, and by further
numerical checks at higher orders. Using these insights, we argue that the
modification of the power spectrum from soft modes corresponds at most to
logarithmic corrections. Finally, we discuss the asymptotic behavior in the
large and small momentum regimes and identify the expansion parameter pertinent
to non-linear corrections.
