Propagating spatially varying multiplicative shear bias to cosmological parameter estimation for stage-IV weak-lensing surveys

We consider the bias introduced by a spatially varying multiplicative shear bias (m-bias) on tomographic cosmic shear angular power spectra. To compute the bias in the power spectra, we estimate the mode-coupling matrix associated with an m-bias map using a computationally efficient pseudo-C-l method. This allows us to consider the effect of the m-bias to high l. We then conduct a Fisher matrix analysis to forecast resulting biases in cosmological parameters. For a Euclid-like survey with a spatially varying m-bias, with zero mean and rms of 0.01, we find that parameter biases reach a maximum of similar to 10 per cent of the expected statistical error, if multipoles up to l(max) = 5000 are included. We conclude that the effect of the spatially varying m-bias may be a subdominant but potentially non-negligible contribution to the error budget in forthcoming weak lensing surveys. We also investigate the dependence of parameter biases on the amplitude and angular scale of spatial variations of the m-bias field, and conclude that requirements should be placed on the rms of spatial variations of the m-bias, in addition to any requirement on the mean value. We find that, for a Euclid-like survey, biases generally exceed similar to 30 per cent of the statistical error for m-bias rms similar to 0.02-0.03 and can exceed the statistical error for rms similar to 0.04-0.05. This allows requirements to be set on the permissible amplitude of spatial variations of the m-bias that will arise due to systematics in forthcoming weak lensing measurements.