Cosmological consequences of intrinsic alignments super-sample covariance

We examine cosmological constraints from high precision weak lensing surveys including super-sample covariance (SSC) due to the finite survey volume. Specifically, we focus on the contribution of {\it beat coupling} in the intrinsic alignments as a part of full cosmic shear signal under flat sky approximation. The SSC-effect grows by going to lower redshift bin and indicates considerable footprint on the intermediate and high multipoles for cumulative signal to noise ratio (SNR). The SNR is reduced by $\approx 10\%$ as a consequence of including the intrinsic alignments super-sample covariance, for the full cosmic shear signal, depending on the amplitude of intrinsic alignments, the ellipticity dispersion and the survey redshift ranges, while the contribution of photometric redshift error can be ignored in the cumulative signal to noise ratio. Using the Fisher-matrix formalism, we find that the impact of large modes beyond the volume of the surveys on the small modes alters the intrinsic alignments. However, corresponding impact on the cosmological parameters estimation is marginal compared to that of for gravitational weak lensing, particularly, when all available redshift bins are considered. Our results also demonstrate that, including SSC-effect on the intrinsic alignments in the analytical covariance matrix of full cosmic shear leads to increase marginally the confidence interval for $\sigma_8$ by $\approx 10\%$ for a sample with almost high intrinsic alignments amplitude.