Precision Comparison of the Power Spectrum in the EFTofLSS with Simulations

TL;DR

This paper evaluates the accuracy of the EFTofLSS in predicting the dark matter power spectrum at two-loop order by comparing it with high-precision simulations, identifying necessary counterterms and assessing the theory's reach.

Contribution

It demonstrates that including three specific counterterms allows the EFTofLSS to match simulation data up to higher wavenumbers than previous methods, extending the analytical control of cosmological data.

Findings

EFTofLSS matches simulation data up to k≈0.34 h/Mpc at z=0

Inclusion of three counterterms is necessary for accuracy

The theory's k-reach exceeds previous analytical techniques

Abstract

We study the prediction of the dark matter power spectrum at two-loop order in the Effective Field Theory of Large Scale Structures (EFTofLSS) using high precision numerical simulations. In our universe, short distance non-linear perturbations, not under perturbative control, affect long distance fluctuations through an effective stress tensor that needs to be parametrized in terms of counterterms that are functions of the long distance fluctuating fields. We find that at two-loop order it is necessary to include three counterterms: a linear term in the over density, $\delta$, a quadratic term, $\delta^2$, and a higher derivative term, $\partial^2\delta$. After the inclusion of these three terms, the EFTofLSS at two-loop order matches simulation data up to $k\simeq 0.34 \,h\, {\rm Mpc}^{-1}$ at redshift $z=0$, up to $k\simeq 0.55\,h\, {\rm Mpc}^{-1}$ at $z=1$, and up to $k\simeq 1.1\,h\, {\rm Mpc}^{-1}$ at $z=2$. At these wavenumbers, the cosmic variance of the simulation is at least as small as $10^{-3}$, providing a high precision comparison between theory and data. The actual reach of the theory is affected by theoretical uncertainties associated to not having included higher order terms in perturbation theory, for which we provide an estimate, and by potentially overfitting the data, which we also try to address. Since in the EFTofLSS the coupling constants associated with the counterterms are unknown functions of time, we show how a simple parametrization gives a sensible description of their time-dependence. Overall, the $k$-reach of the EFTofLSS is much larger than previous analytical techniques, showing that the amount of cosmological information amenable to high-precision analytical control might be much larger than previously believed.