Large-scale structure of the Universe and cosmological perturbation theory

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 correlations 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.

The Effective Field Theory of Large Scale Structures at two loops

“…The loop corrections to the power spectrum in SPT are conventionally written in terms of separate diagrams, which themselves are integrals of factors of P 11 times symmetrized kernels F (s) n and G (s) n that can be obtained from recurrence relations (see, e.g., [3]). The separate diagrams also have different properties in the UV.…”

“…Since we are interested in computing correlation functions for δ(k) 1 or equivalently k k NL , this perturbation theory is manifestly convergent. The effective theory differs from the so-called standard perturbation theory (SPT), and relatives (see for example [3,4] or [5]), by additional terms in the equations of motion for the overdensities that parameterize relevant short-distance physics. Approximately, these can be thought of as corrections to the fluid equations of motion in the form of speed of sound, viscosity, and stochastic pressure.…”

“…This is what in quantum field theory is referred to as decoupling. However, this is a property of all physics, and not just of quantum field theory 3 . The presence of this artificial cutoff at ∼ 3 h Mpc −1 introduces some spurious cutoff dependence in our two-loop result that we must remove with a two-loop contribution to the EFT parameter relevant to one loop.…”

The properties of cosmic velocity fields

“…Then, in the case of Newtonian gravity, the acceleration is given by the gradient of the gravitational potential φ. Hence, the single stream motion of a Lagrangian fluid element (xq, vq) is curl-free non-perturbatively at all times since at fixed q: Bernardeau et al 2002). After shell-crossing, various fluid elements overlap and vorticity emerges (cf.…”

Non-Gaussianity of the density distribution in accelerating universes: II.N-body simulations

“…Since it is known that the scaling < δ n > c ∝ σ 2n−2 holds for weakly non-linear region, if we consider the gravitational clustering from Gaussian initial conditions [30], we introduce the following higher-order statistical quantities [1,2]:…”