Projection of the gravitational dynamics on a subspace of probability distributions: curl-free Gaussian ansatz
Résumé
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 autopower spectra also follows from the equations of motion. Although the density power spectrum is only recovered up to a smooth drift on baryon acoustic oscillation (BAO) scales, the predicted density correlation function agrees with numerical simulations within 2% from BAO scales down to 7h-1 Mpc at z≥0.35, without any free parameter. Thus, this parameter-free extension of the Zeldovich approximation is not competitive with other schemes for the power spectrum, but it provides a good prediction for the correlation function. However, the improvement over the standard Zeldovich approximation remains rather modest. This means that including non-Gaussianities will be essential to significantly improve analytical predictions within this general framework.