Systematic study of projection biases in the weak lensing analysis of cosmic shear and the combination of galaxy clustering and galaxy-galaxy lensing

This paper presents the results of a systematic study of projection biases in the weak lensing analysis of cosmic shear and the combination of galaxy clustering and galaxy-galaxy lensing using data collected during the first year of running the Dark Energy Survey experiment. The study uses Lambda cold dark matter ($\mathrm{\ensuremath{\Lambda}}\text{CDM}$) as the cosmological model and two-point correlation functions for the weak lensing (WL) analysis. The results in this paper show that, independent of the WL analysis, projection biases of more than $1\ensuremath{\sigma}$ exist and are a function of the position of the true values of the parameters $h$, ${n}_{s}$, ${\mathrm{\ensuremath{\Omega}}}_{b}$, and ${\mathrm{\ensuremath{\Omega}}}_{\ensuremath{\nu}}{h}^{2}$ with respect to their prior probabilities. For cosmic shear, and the combination of galaxy clustering and galaxy-galaxy lensing, this study shows that the coverage probability of the 68.27% credible intervals ranges from as high as 93% to as low as 16% and that these credible intervals are inflated, on average, by 29% for cosmic shear and 20% for the combination of galaxy clustering and galaxy-galaxy lensing. The results of the study also show that, in six out of nine tested cases, the reduction in error bars obtained by transforming credible intervals into confidence intervals is equivalent to an increase in the amount of data by a factor of 3.