As recently shown by Viola et al., the common (KSB) method for measuring weak
gravitational shear creates a non-linear relation between the measured and the
true shear of objects. We investigate here what effect such a non-linear
calibration relation may have on cosmological parameter estimates from weak
lensing if a simpler, linear calibration relation is assumed. We show that the
non-linear relation introduces a bias in the shear-correlation amplitude and
thus a bias in the cosmological parameters Omega_matter and sigma_8. Its
direction and magnitude depends on whether the point-spread function is narrow
or wide compared to the galaxy images from which the shear is measured.
Substantial over- or underestimates of the cosmological parameters are equally
possible, depending also on the variant of the KSB method. Our results show
that for trustable cosmological-parameter estimates from measurements of weak
lensing, one must verify that the method employed is free from
ellipticity-dependent biases or monitor that the calibration relation inferred
from simulations is applicable to the survey at hand.Comment: 5 pages, 3 figures, submitted to A&
