The unequal-time matter power spectrum: impact on weak lensing observables

TL;DR

This paper examines how using single-epoch matter power spectra affects weak lensing observables, comparing various approximations and providing new fitting functions, revealing significant deviations at large scales relevant for current and future surveys.

Contribution

It introduces a new fitting function for the evolution of EFT counterterms and evaluates the impact of different approximations on weak lensing power spectra.

Findings

Limber's approximation diverges at large scales ($\,\ell<10$).

Deviations from exact calculations reach up to 2% for cosmic lensing.

The analysis pipeline is publicly available as the unequalpy Python package.

Abstract

We investigate the impact of a common approximation on weak lensing power spectra: the use of single-epoch matter power spectra in integrals over redshift. We disentangle this from the closely connected Limber's approximation. We derive the unequal-time matter power spectrum at one-loop in standard perturbation theory and effective field theory to deal with non-linear physics. We compare these formalisms and conclude that the unequal-time power spectrum using effective field theory breaks for larger scales. As an alternative, we introduce the midpoint approximation. We also provide, for the first time, a fitting function for the time evolution of the effective field theory counterterms based on the Quijote simulations. Then we compute the angular power spectrum using a range of approaches: the Limber's approximation, and the geometric and midpoint approximations. We compare our results with the exact calculation at all angular scales using the unequal-time power spectrum. We use DES Y1 and LSST-like redshift distributions for our analysis. We find that the use of the Limber's approximation in weak lensing diverges from the exact calculation of the angular power spectrum on large-angle separations, $\ell < 10$. Even though this deviation is of order $2\%$ maximum for cosmic lensing, we find the biggest effect for galaxy clustering and galaxy-galaxy lensing. We show that not only is this true for upcoming galaxy surveys, but also for current data such as DES Y1. Finally, we make our pipeline and analysis publicly available as a Python package called unequalpy.