TY - JOUR

T1 - Divergence of perturbation theory in large scale structures

AU - Pajer, Enrico

AU - Woude, Drian Van Der

PY - 2018/5/14

Y1 - 2018/5/14

N2 - We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for which exact solutions before shell crossing are known. We review the convergence of perturbation theory for the power spectrum, recently proven by McQuinn and White [1], and extend it to non-Gaussian initial conditions and the bispectrum. In contrast, we prove that perturbation theory diverges for the real space two-point correlation function and for the probability density function (PDF) of the density averaged in cells and all the cumulants derived from it. We attribute these divergences to the statistical averaging intrinsic to cosmological observables, which, even on very large and "perturbative" scales, gives non-vanishing weight to all extreme fluctuations. Finally, we discuss some general properties of non-perturbative effects in real space and Fourier space.

AB - We make progress towards an analytical understanding of the regime of validity of perturbation theory for large scale structures and the nature of some non-perturbative corrections. We restrict ourselves to 1D gravitational collapse, for which exact solutions before shell crossing are known. We review the convergence of perturbation theory for the power spectrum, recently proven by McQuinn and White [1], and extend it to non-Gaussian initial conditions and the bispectrum. In contrast, we prove that perturbation theory diverges for the real space two-point correlation function and for the probability density function (PDF) of the density averaged in cells and all the cumulants derived from it. We attribute these divergences to the statistical averaging intrinsic to cosmological observables, which, even on very large and "perturbative" scales, gives non-vanishing weight to all extreme fluctuations. Finally, we discuss some general properties of non-perturbative effects in real space and Fourier space.

KW - cosmic flows

KW - cosmological parameters from LSS

KW - cosmological perturbation theory

KW - power spectrum

UR - http://www.scopus.com/inward/record.url?scp=85048129558&partnerID=8YFLogxK

U2 - 10.1088/1475-7516/2018/05/039

DO - 10.1088/1475-7516/2018/05/039

M3 - Article

AN - SCOPUS:85048129558

SN - 1475-7516

VL - 2018

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

IS - 5

M1 - 039

ER -