The Effective Field Theory and Perturbative Analysis for Log-Density Fields

TL;DR

This paper develops an effective field theory and perturbative analysis for the log-density field, demonstrating improved convergence and accuracy in modeling the matter power spectrum on large scales, with implications for accessing smaller scale information.

Contribution

It introduces a novel perturbation series directly for the log-density field, improving convergence and modeling accuracy over traditional methods.

Findings

Perturbation theory for the log-density field converges faster and better on large scales.

A small number of parameters can capture the large-scale behavior of the log-density power spectrum.

The model achieves percent-level accuracy up to k ≈ 0.38 Mpc^{-1}h at z=0.

Abstract

A logarithm transformation over the matter overdensity field $\delta$ brings information from the bispectrum and higher-order n-point functions to the power spectrum. We calculate the power spectrum for the log-transformed field $A$ at one, two and three loops using perturbation theory (PT). We compare the results to simulated data and give evidence that the PT series is asymptotic already on large scales, where the $k$ modes no longer decouple. This motivates us to build an alternative perturbative series for the log-transformed field that is not constructed on top of perturbations of $\delta$ but directly over the equations of motion for $A$ itself. This new approach converges faster and better reproduces the large scales at low $z$. We then show that the large-scale behaviour for the log-transformed field power spectrum can be captured by a small number of free parameters. Finally, we add the counter-terms expected within the effective field theory framework and show that the theoretical model, together with the IR-resummation procedure, agrees with the measured spectrum with percent precision until $k \simeq 0.38 $ Mpc$^{-1}$h at $z=0$. It indicates that the non-linear transformation indeed linearizes the density field and, in principle, allows us to access information contained on smaller scales.