Matching Cosmic Shear Analysis in Harmonic and Real Space

Recent cosmic shear analyses have exhibited discrepancies of up to $1\sigma$ between the inferred cosmological parameters when analyzing summary statistics in real space versus harmonic space. In this paper, we demonstrate the consistent measurement and analysis of cosmic shear two-point functions in harmonic and real space using the $i${\sc Master} algorithm. This algorithm provides a unified prescription to model the survey window effects and scale cuts in both real space (due to observational systematics) and harmonic space (due to model limitations), resulting in a matching estimation of the cosmic shear power spectrum from both harmonic and real space estimators. We show that the $i$\textsc{Master} algorithm gives matching results using measurements from the HSC Y1 mock shape catalogs in both real and harmonic space, resulting in matching inferences of $S_8=\sigma_8(\Omega_m/0.3)^{0.5}$. This method provides an unbiased estimate of the cosmic shear power spectrum, and $S_8$ inference that has a correlation coefficient of 0.997 between analyses using measurements in real space and harmonic space when $S_8$ is the only free parameter. We observe the mean difference between the two inferred $S_8$ values to be 0.0004 across noise-free mock realizations, far below the observed difference of 0.042 for the published HSC Y1 analyses and well below the statistical uncertainties. While the notation employed in this paper is specific to photometric galaxy surveys, the methods are equally applicable and can be extended to spectroscopic galaxy surveys, intensity mapping, and CMB surveys.