Large scale structure of the universe and cosmological perturbation theory

By F. Bernardeau, Stéphane Colombi, Enrique Gaztañaga, R. Scoccimarro. 2001

1,489 citations recorded by the source corpus.

Abstract We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitational instability, from the linear to the non-linear regime. This includes Eulerian and Lagrangian PT, non-linear approximations, and a brief description of numerical simulation techniques. We then cover the basic statistical tools used in cosmology to describe cosmic fields, such as correlation functions in real and Fourier space, probability distribution functions, cumulants and generating functions. In subsequent sections we review the use of PT to make quantitative predictions about these statistics according to initial conditions, including effects of possible non-Gaussianity of the primordial fields. Results are illustrated by detailed comparisons of PT predictions with numerical simulations. The last sections deal with applications to observations. First, we review in detail practical estimators of statistics in galaxy catalogs and related errors, including traditional approaches and more recent developments. Then, we consider the effects of the bias between the galaxy distribution and the matter distribution, the treatment of redshift distortions in three-dimensional surveys and of projection effects in angular catalogs, and some applications to weak gravitational lensing. We finally review the current observational situation regarding statistics in galaxy catalogs and what the future generation of galaxy surveys promises to deliver.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/095b683676eacbdc1aa7ad53d3a1cd9ce1a37567

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Citations in the corpus

Equivalence Principle and the Baryon Acoustic Peak (2015, background): “where Fn are the usual Standard Perturbation Theory (SPT) kernels [1]:”
Cosmological parameters from lensing power spectrum and bispectrum tomography (2003, background): “In the weakly non-linear regime (δ <∼ 1), the evolution of mass clustering can be described by perturba ion theory (e.g., Bernardeau et al. 2002).”
Primordial black holes and gravitational waves from parametric amplification of curvature perturbations (2019, background): “[23{43]. Primordial curvature perturbations from quantum uctuations during in ation can seed large-scale structure and explain the cosmic microwave background(CMB) temperature anisotropy successfully [44,45]. On CMB scales the amplitude of the power spectrum of curvature perturbations is found to be”
The Initial Conditions of the Universe from Constrained Simulations (2012, background): “For technical detailswe refer to Buchert (1994); Bouchet et al. (1995); Bernardeau et al. (2002).”
Multi-scale initial conditions for cosmological simulations (2011, methodology): “For details, we kindly refer the reader to the wide field of existing literature on LPT (e.g. Buchert, Melott & Weiss 1994; Bouchet et al. 1995; Scoccimarro 1998; Bernardeau et al. 2002).”
Gravity and Large-Scale Nonlocal Bias (2012, methodology): “In what follows, we will make heavy use of results from perturbation theory (PT, see [48] for a review).”
BOSS DR12 full-shape cosmology: ΛCDM constraints from the large-scale galaxy power spectrum and bispectrum monopole (2021, background): “As the Universe evolves, gravitational evolution induces non-Gaussianity [e.g., 3], aﬀording a complex matter distribution, with information distributed over a broad range of statistics.”
Cosmological parameters from the BOSS galaxy power spectrum (2019, background): “where the redshift-space kernels are given by [22],”
Neutrino Mass in Cosmology: Status and Prospects (2011, background): “In the same vein, the one-loop corrections (50) are often also extended to ΛCDM cosmologies without further modification [62].”
THE COYOTE UNIVERSE. I. PRECISION DETERMINATION OF THE NONLINEAR MATTER POWER SPECTRUM (2008, background): “Perturbation theory has errors on the mass power spectrum currently estimated to be at the percent level in the weakly nonlinear regime (see, e.g., Jeong & Komatsu 2006; Carlson et al. 2009 for recent treatments or Bernardeau et al. 2002 for an earlier review).”
Towards an accurate model of the redshift-space clustering of haloes in the quasi-linear regime (2011, methodology): “We refer the reader to Bernardeau et al. (2002) for an introduction to standard perturbation theory.”
On the statistics of biased tracers in the Effective Field Theory of Large Scale Structures (2015, neutral): “= Z d3q 1 (2ˇ) 3 d 3q 2 (2ˇ) dq 3 (2ˇ)3 F(3) s (q 1 ;q 2 ;q 3 ) (3) D (k (1)q 1 q 2 q 3 ) (q 1 ;t) (1)(q 2 ;t) (1)(q 3 ;t) ; and F(n) s are standard Eulerian perturbation theory kernels (see e.g. [23] for denitions). By analogy, for the overdensity eld of biased tracers it is useful to rewrite (10) ”