Unequal-Time Correlators for Cosmology

TL;DR

This paper examines the impact of using equal-time approximations for unequal-time correlators in large-scale structure surveys, revealing potential biases in weak lensing cosmology, especially at large redshift separations.

Contribution

It introduces an analysis of unequal-time correlators using perturbation theory and simulations, highlighting the limitations of the geometric mean approximation in cosmological measurements.

Findings

Impact of equal-time approximation increases at large redshift separations (>0.3).

Potential biases in cosmic shear power spectrum predictions for Euclid/LSST-like surveys.

Corrections require advanced perturbation theory or extensive simulations.

Abstract

Measurements of the power spectrum from large-scale structure surveys have to date assumed an equal-time approximation, where the full cross-correlation power spectrum of the matter density field evaluated at different times (or distances) has been approximated either by the power spectrum at a fixed time, or in an improved fashion, by a geometric mean $P(k; r_1, r_2)=[P(k; r_1) P(k; r_2)]^{1/2}$. In this paper we investigate the expected impact of the geometric mean ansatz, and present an application in assessing the impact on weak gravitational lensing cosmological parameter inference, using a perturbative unequal-time correlator. As one might expect, we find that the impact of this assumption is greatest at large separations in redshift $\Delta z > 0.3$ where the change in the amplitude of the matter power spectrum can be as much as $10$ percent for $k > 5h$Mpc$^{-1}$. However, of more concern is that the corrections for small separations, where the clustering is not close to zero, may not be negligibly small. In particular, we find that for a Euclid- or LSST-like weak lensing experiment the assumption of equal-time correlators may result in biased predictions of the cosmic shear power spectrum, and that the impact is strongly dependent on the amplitude of the intrinsic alignment signal. To compute unequal-time correlations to sufficient accuracy will require advances in either perturbation theory to high $k$-modes, or extensive use of simulations.