  Intrinsic alignments (IA) of galaxies have been recognized as one of the most
serious contaminants to weak lensing. These systematics need to be isolated and
mitigated in order for ongoing and future lensing surveys to reach their full
potential. The IA self-calibration (SC) method was shown in previous studies to
be able to reduce the GI contamination by up to a factor of 10 for the 2-point
and 3-point correlations. The SC method does not require to assume an IA model
in its working and can extract the GI signal from the same photo-z survey
offering the possibility to test and understand structure formation scenarios
and their relationship to IA models. In this paper, we study the effects of the
IA SC mitigation method on the precision and accuracy of cosmological parameter
constraints from future cosmic shear surveys LSST, WFIRST and Euclid. We
perform analytical and numerical calculations to estimate the loss of precision
and the residual bias in the best fit cosmological parameters after the
self-calibration is performed. We take into account uncertainties from
photometric redshifts and the galaxy bias. We find that the confidence contours
are slightly inflated from applying the SC method itself while a significant
increase is due to the inclusion of the photo-z uncertainties. The bias of
cosmological parameters is reduced from several-$\sigma$, when IA is not
corrected for, to below 1-$\sigma$ after SC is applied. These numbers are
comparable to those resulting from applying the method of marginalizing over IA
model parameters despite the fact that the two methods operate very
differently. We conclude that implementing the SC for these future cosmic-shear
surveys will not only allow one to efficiently mitigate the GI contaminant but
also help to understand their modeling and link to structure formation.
