Projection of the gravitational dynamics on a subspace of probability distributions: curl-free Gaussian ansatz

Abstract

We present a new approach to model the gravitational dynamics of large-scale structures. Instead of solving the equations of motion up to a finite perturbative order or building phenomenological models, we follow the evolution of the probability distribution of the displacement and velocity fields within an approximation subspace. Keeping the exact equations of motion with their full nonlinearity, this provides a nonperturbative scheme that goes beyond shell crossing. Focusing on the simplest case of a curl-free Gaussian ansatz for the displacement and velocity fields, we find that truncations of the power spectra on nonlinear scales directly arise from the equations of motion. This leads to a truncated Zeldovich approximation for the density power spectrum, but with a truncation that is not set a priori and with different power spectra for the displacement and velocity fields. The positivity of their auto power spectra also follows from the equations of motion. Although the density power spectrum is only recovered up to a smooth drift on BAO scales, the predicted density correlation function agrees with numerical simulations within $2\%$ from BAO scales down to $7h^{-1}\mathrm{Mpc}$ at $z\ge 0.35$, without any free parameter.

25 pages

References in corpus (18)

• The Effective Field Theory of Cosmological Large Scale Structures
• Resumming Cosmological Perturbations via the Lagrangian Picture: One-loop Results in Real Space and in Redshift Space
• On the Robustness of the Acoustic Scale in the Low-Redshift Clustering of Matter
• Cosmology with Weak Lensing Surveys
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Observational systematics and baryon acoustic oscillations in the correlation function
• A critical look at cosmological perturbation theory techniques
• Generation of Vorticity and Velocity Dispersion by Orbit Crossing
• Flowing with Time: a New Approach to Nonlinear Cosmological Perturbations
• Multi-Point Propagators in Cosmological Gravitational Instability
• A Closure Theory for Non-linear Evolution of Cosmological Power Spectra
• Analytic Prediction of Baryonic Effects from the EFT of Large Scale Structures
• Large-N expansions applied to gravitational clustering
• Lagrangian perturbation theory at one loop order: successes, failures, and improvements
• Using the Zeldovich dynamics to test expansion schemes
• Propagators in Lagrangian space
• Large-scale structure perturbation theory without losing stream crossing
• Expansion schemes for gravitational clustering: computing two-point and three-point functions
• Galilean invariant resummation schemes of cosmological perturbations

Cited by in corpus (2)

• Accurate initial conditions for cosmological N-body simulations: Minimizing truncation and discreteness errors
• Lagrangian-space Gaussian ansatz for the matter redshift-space power spectrum and correlation function