Perturbation theory, effective field theory, and oscillations in the power spectrum

TL;DR

This paper investigates the connection between nonlinear matter power spectra and perturbation theories, demonstrating effective field theory's advantages and testing models on oscillation predictions, including BAO and string monodromy models.

Contribution

It establishes a unified EFT-based parametrization for LPT and SPT, compares their convergence, and evaluates their effectiveness in modeling primordial oscillations in the power spectrum.

Findings

EFT parametrization has a larger radius of convergence than SPT.

LPT models with EFT-inspired parametrization exhibit running with k in 3D.

Most models successfully predict oscillations beyond their original PT versions.

Abstract

We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the results of effective field theory (EFT), and can thus be expanded in terms of the same parameters. We find that its radius of convergence is larger than the SPT loop expansion. The same EFT parametrization applies to all SPT loop terms and, if stochasticity can be ignored, to all N-point correlators. In 3-d, the LPT structure is considerably more complicated, and we find that LPT models with parametrization motivated by the EFT exhibit running with $k$ and that SPT is generally a better choice. Since these transfer function expansions contain free parameters that change with cosmological model their usefulness for broadband power is unclear. For this reason we test the predictions of these models on baryonic acoustic oscillations (BAO) and other primordial oscillations, including string monodromy models, for which we ran a series of simulations with and without oscillations. Most models are successful in predicting oscillations beyond their corresponding PT versions, confirming the basic validity of the model.