Relation between standard perturbation theory and regularized multi-point propagator method

TL;DR

This paper compares the regularized multi-point propagator method with standard perturbation theory, showing that the latter often provides more accurate predictions for nonlinear matter evolution, especially at high wavenumbers, and proposes a divergence-free modification.

Contribution

It offers an alternative explanation for Reg PT within standard perturbation theory and introduces a modified version that avoids divergence at small scales.

Findings

Standard perturbation theory outperforms Reg PT at high-k regions.

Solutions of standard perturbation theory better match N-body simulations.

Proposed a divergence-free modification of standard perturbation theory.

Abstract

We investigate the relation between the regularized multi-propagator method, called "Reg PT", and the standard perturbation theory. Reg PT is one of the most successful models to describe nonlinear evolution of dark matter fluctuations. However, Reg PT is a mathematically unproven interpolation formula between the large-scale solution calculated by the standard perturbation theory and the limiting solution in the small scale calculated by the multi-point propagator method. In this paper, we give an alternative explanation for Reg PT in the context of the standard perturbation theory, showing that Reg PT does not ever have more effective information on nonlinear matter evolution than the standard perturbation theory. In other words, the solutions of the standard perturbation theory reproduce the results of $N$-body simulations better than those of Reg PT, especially at the high-$k$ region. This fact means that the standard perturbation theory at the two-loop level is still one of the best predictions of the nonlinear power spectrum to date. Nevertheless, the standard perturbation theory has not been preferred because of the divergent behavior of the solution at small scales. To solve this problem, we also propose a modified standard perturbation theory which avoids the divergence.