Assessing theoretical uncertainties for cosmological constraints from weak lensing surveys

TL;DR

This paper compares various theoretical models and simulations for predicting weak lensing signals, assessing their accuracy for current and future cosmological surveys to ensure reliable parameter constraints.

Contribution

It provides a comprehensive comparison of fitting functions, emulators, and simulations for weak lensing predictions, highlighting their accuracy and limitations for stage III and IV surveys.

Findings

Fitting functions agree within 0.3σ for stage III surveys

Agreement increases to 1.4-3.0σ for stage IV surveys

Mead fitting function shows the best agreement with emulators

Abstract

$ $Weak gravitational lensing is a powerful probe which is used to constrain the standard cosmological model and its extensions. With the enhanced statistical precision of current and upcoming surveys, high accuracy predictions for weak lensing statistics are needed to limit the impact of theoretical uncertainties on cosmological parameter constraints. For this purpose, we present a comparison of the theoretical predictions for the nonlinear matter and weak lensing power spectra, based on the widely used fitting functions ($\texttt{mead}$ and $\texttt{rev-halofit}$), emulators ($\texttt{EuclidEmulator}$, $\texttt{EuclidEmulator2}$, $\texttt{BaccoEmulator}$ and $\texttt{CosmicEmulator}$) and N-body simulations ($\texttt{Pkdgrav3}$). We consider the forecasted constraints on the $\Lambda \texttt{CDM}$ and $\texttt{wCDM}$ models from weak lensing for stage III and stage IV surveys. We study the relative bias on the constraints and their dependence on the assumed prescriptions. Assuming a $\Lambda \texttt{CDM}$ cosmology, we find that the relative agreement on the $S_8$ parameter is between $0.2-0.3\sigma$ for a stage III-like survey between the above predictors. For a stage IV-like survey the agreement becomes $1.4-3.0\sigma$. In the $\texttt{wCDM}$ scenario, we find broader $S_8$ constraints, and agreements of $0.18-0.26\sigma$ and $0.7-1.7\sigma$ for stage III and stage IV surveys, respectively. The accuracies of the above predictors therefore appear adequate for stage III surveys, while the fitting functions would need improvements for future stage IV weak lensing surveys. Furthermore, we find that, of the fitting functions, $\texttt{mead}$ provides the best agreement with the emulators. We discuss the implication of these findings for the preparation of the future weak lensing surveys.