Large-scale structure perturbation theory without losing stream crossing

TL;DR

This paper introduces a novel perturbation theory approach for large-scale cosmic structure that inherently includes stream crossing, improving accuracy over traditional methods and aligning better with simulations.

Contribution

It develops a perturbative framework that accounts for stream crossing from the outset, with exact calculations for deviations from Zel'dovich evolution, enhancing modeling of cosmic clustering.

Findings

One-loop displacement and density power spectra show improved agreement with N-body simulations in 1D.

The method effectively incorporates stream crossing effects.

Potential for better modeling in higher dimensions without additional parameters.

Abstract

We suggest an approach to perturbative calculations of large-scale clustering in the Universe that includes from the start the stream crossing (multiple velocities for mass elements at a single position) that is lost in traditional calculations. Starting from a functional integral over displacement, the perturbative series expansion is in deviations from (truncated) Zel'dovich evolution, with terms that can be computed exactly even for stream-crossed displacements. We evaluate the one-loop formulas for displacement and density power spectra numerically in 1D, finding dramatic improvement in agreement with N-body simulations compared to the Zel'dovich power spectrum (which is exact in 1D up to stream crossing). Beyond 1D, our approach could represent an improvement over previous expansions even aside from the inclusion of stream crossing, but we have not investigated this numerically. In the process we show how to achieve effective-theory-like regulation of small-scale fluctuations without free parameters.