On the non-linear scale of cosmological perturbation theory

Apr 4, 2013
38 pages
Published in:
  • JCAP 09 (2013) 024
  • Published: Sep 23, 2013
e-Print:
Report number:
  • CERN-PH-TH-2013-062,
  • DESY-13-060

Citations per year

201320162019202220240246810
Abstract: (IOP)
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 at any order in perturbation theory. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.
Note:
  • 38 pages, 11 figures; v2 minor changes, references added. Matches published version
  • power spectrum
  • baryon acoustic oscillations
  • correction: nonlinear
  • approximation: eikonal
  • oscillation: acoustic
  • power spectrum
  • perturbation theory
  • enhancement
  • correlation function
  • asymptotic behavior