Cosmology with second and third-order shear statistics for the Dark Energy Survey: Methods and simulated analysis

Abstract

We present a new pipeline designed for the robust inference of cosmological parameters using both second- and third-order shear statistics. We build a theoretical model for rapid evaluation of three-point correlations using our fastnc code and integrate it into the CosmoSIS framework. We measure the two-point functions $ξ_{\pm}$ and the full configuration-dependent three-point shear correlation functions across all auto- and cross-redshift bins. We compress the three-point functions into the mass aperture statistic $\langle M_{\rm ap}^3\rangle$ for a set of 796 simulated shear maps designed to model the Dark Energy Survey (DES) Year 3 data. We estimate from it the full covariance matrix and model the effects of intrinsic alignments, shear calibration biases and photometric redshift uncertainties. We apply scale cuts to minimize the contamination from the baryonic signal as modeled through hydrodynamical simulations. We find a significant improvement of $83\%$ on the Figure of Merit in the $Ω_{\rm m}$-$S_8$ plane when we add the $\langle M_{\rm ap}^3\rangle$ data to the $ξ_{\pm}$ information. We present our findings for all relevant cosmological and systematic uncertainty parameters and discuss the complementarity of third-order and second-order statistics.

Figures (15)

• Figure 1: Dispersion of mass aperture emulator predictions. On the y-axis we show the percentage error of the network predictions relative to their corresponding target values. The green lines mark the interval between -0.29% and 0.29%, and the magenta between -1.02% and 1.02%. A total of $99\%$ of the samples lie between the green lines, and $100\%$ of them between the magenta lines, showing that the emulator scatter is a negligible source of error for our $\langle\mathcal{M}_{\rm ap}^3\rangle$ model.
• Figure 2: Mass aperture statistic data vector for simulated analysis. Panels show the aperture mass statistic as a function of filter radii $\theta$ for different redshift-bin combinations $(i,j,k)$ indicated on the upper right corner of each panel. The green line indicates our synthetic data vector computed from our pipeline at CosmoGridV1 cosmology. The error bars are estimated from the measured covariance. We also include a red line indicating a theoretical calculation with an artificially increased intrinsic alignment signal to show the effect of this systematic on third-order statistics. We use $A_1=1.0$ and $\alpha_1=0.5$, and find that this is more relevant for the lower redshift bins.
• Figure 3: Covariance of second order shear correlation functions. The upper triangle is the analytic result, and the lower triangle is measured from 796 CosmoGridV1 simulations. The covariances are consistent, having sufficiently close amplitude and structure.
• Figure 4: Covariance of the aperture mass statistics estimated from 796 CosmoGridV1 simulations. The number indicated by the ticks on x- and y-axes are the triplets of the redshift bins. The off-diagonal structure amounts mostly to cross-correlations between different aperture filters for the same or nearby redshift bin combinations. This is expected, given that there is overlap between the 3PCF contributions to the $\langle\mathcal{M}_{\rm ap}^3\rangle$ integral at different filters. We check the convergence of this covariance in Appendix \ref{['sec:appendix-convergence']}
• Figure 5: Cross-covariance between the two-point functions and the aperture mass statistics estimated from 796 CosmoGridV1 simulations. The numbers indicated by the ticks on x/y axes are the pairs/triplets of the redshift bins. The lack of noticeable cross-correlation even for the same redshifts is due to the S/N discrepancy between the statistics.