Asymptotic expansions for the Large Scale Structure

Abstract

We explore the deep ultraviolet (that is, short-distance) limit of the power spectrum (PS) and of the correlation function of a cold dark matter dominated Universe. While for large scales the PS can be written as a double series expansion, in powers of the linear PS and of the wavenumber $k$, we show that, in the opposite limit, it can be expressed via an expansion in powers of the form $1/k^{d+2n}$, where $d$ is the number of spatial dimensions, and $n$ is a non negative integer. The coefficients of the terms of the expansion are nonperturbative in the linear PS, and can be interpreted in terms of the probability density function for the displacement field, evaluated around specific configurations of the latter, that we identify. In the case of the Zel'dovich dynamics, these coefficients can be determined analytically, whereas for the exact dynamics they can be treated as fit, or nuisance, parameters. We confirm our findings with numerical simulations and discuss the necessary steps to match our results to those obtained for larger scales and to actual measurements.

arXiv comment27 pages, 12 figures

References in corpus (23)

• Efficient Computation of CMB anisotropies in closed FRW models
• Halo Models of Large Scale Structure
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• First results from the IllustrisTNG simulations: matter and galaxy clustering
• Cosmological Non-Linearities as an Effective Fluid
• The Effective Field Theory of Cosmological Large Scale Structures
• A Lagrangian effective field theory
• First star-forming structures in fuzzy cosmic filaments
• Combining perturbation theories with halo models
• Cosmological perturbation theory at three-loop order
• Galaxy Formation with BECDM -- II. Cosmic Filaments and First Galaxies
• Coarse-Grained Cosmological Perturbation Theory
• Cosmological perturbation theory in 1+1 dimensions
• Halo Zeldovich model and perturbation theory: dark matter power spectrum and correlation function
• Impact of shell crossing and scope of perturbative approaches in real and redshift space
• Post-collapse perturbation theory in 1D cosmology -- beyond shell-crossing
• Large-scale structure perturbation theory without losing stream crossing
• Shell-crossing in quasi-one-dimensional flow
• A coarse grained perturbation theory for the Large Scale Structure, with cosmology and time independence in the UV
• Structure formation beyond shell-crossing: nonperturbative expansions and late-time attractors
• Lagrangian cosmological perturbation theory at shell-crossing
• Divergence of Perturbation Theory in Large Scale Structures
• A Robust BAO Extractor

Cited by in corpus (11)

• Cosmological perturbations for two cold fluids in $\Lambda$CDM
• Shell-crossing in a $\Lambda$CDM Universe
• Cosmological Vlasov-Poisson equations for dark matter: Recent developments and connections to selected plasma problems
• One-Dimensional Fuzzy Dark Matter Models: Structure Growth and Asymptotic Dynamics
• Kinetic Field Theory for Cosmic Structure Formation
• On the asymptotic behaviour of cosmic density-fluctuation power spectra of cold dark matter
• Renormalization group and UV completion of cosmological perturbations: Gravitational collapse as a critical phenomenon
• On the asymptotic behaviour of cosmic density-fluctuation power spectra
• Gravitational Turbulence: the Small-Scale Limit of the Cold-Dark-Matter Power Spectrum
• Free Cosmic Density Bispectrum on Small Scales
• (1+1)-Dimensional Schrödinger-Poisson equation with contact interaction