Cosmological perturbation theory at three-loop order

TL;DR

This paper investigates the three-loop order in cosmological perturbation theory for the dark matter power spectrum, revealing convergence issues at late times and proposing a technique to improve the series' convergence, with validation against N-body simulations.

Contribution

It introduces a novel method to restore convergence in three-loop perturbation theory for large scale structure, enhancing accuracy in the baryonic acoustic oscillation range.

Findings

Loop expansion does not converge at late times for large scales.

Proposed technique improves convergence for relevant momenta.

Good agreement with N-body simulation data within the BAO range.

Abstract

We analyze the dark matter power spectrum at three-loop order in standard perturbation theory of large scale structure. We observe that at late times the loop expansion does not converge even for large scales (small momenta) well within the linear regime, but exhibits properties compatible with an asymptotic series. We propose a technique to restore the convergence in the limit of small momentum, and use it to obtain a perturbative expansion with improved convergence for momenta in the range where baryonic acoustic oscillations are present. Our results are compared with data from N-body simulations at different redshifts, and we find good agreement within this range.