Cosmological perturbation theory in 1+1 dimensions

TL;DR

This paper explores the limitations of standard Eulerian perturbation theory in cosmology by analyzing a simplified 1D model, demonstrating the advantages of effective theories and Lagrangian approaches in capturing large-scale dynamics.

Contribution

It provides a detailed analysis of 1D gravitational sheets to illustrate the convergence of perturbation theories and highlights the effectiveness of effective equations over traditional methods.

Findings

Eulerian perturbation theory converges to the Zeldovich approximation in 1D.

Standard perturbation theories fail to accurately describe the matter power spectrum.

Effective theories better capture the dynamics of large-scale structures.

Abstract

Many recent studies have highlighted certain failures of the standard Eulerian-space cosmological perturbation theory (SPT). Its problems include (1) not capturing large-scale bulk flows [leading to an O(1) error in the 1-loop SPT prediction for the baryon acoustic peak in the correlation function], (2) assuming that the Universe behaves as a pressureless, inviscid fluid, and (3) treating fluctuations on scales that are non-perturbative as if they were. Recent studies have highlighted the successes of perturbation theory in Lagrangian space or theories that solve equations for the effective dynamics of smoothed fields. Both approaches mitigate some or all of the aforementioned issues with SPT. We discuss these physical developments by specializing to the simplified 1D case of gravitationally interacting sheets, which allows us to substantially reduces the analytic overhead and still (as we show) maintain many of the same behaviors as in 3D. In 1D, linear-order Lagrangian perturbation theory ("the Zeldovich approximation") is exact up to shell crossing, and we prove that n^{th}-order Eulerian perturbation theory converges to the Zeldovich approximation as n goes to infinity. In no 1D cosmology that we consider (including a CDM-like case and power-law models) do these theories describe accurately the matter power spectrum on any mildly nonlinear scale. We find that theories based on effective equations are much more successful at describing the dynamics. Finally, we discuss many topics that have recently appeared in the perturbation theory literature such as beat coupling, the shift and smearing of the baryon acoustic oscillation feature, and the advantages of Fourier versus configuration space. Our simplified 1D case serves as an intuitive review of these perturbation theory results.