Simultaneous Constraints on Cosmology and Photometric Redshift Bias from
  Weak Lensing and Galaxy Clustering
  We investigate the expected cosmological constraints from a combination of
weak lensing and large-scale galaxy clustering using realistic redshift
distributions. Introducing a systematic bias in the weak lensing redshift
distributions (of 0.05 in redshift) produces a $>2\sigma$ bias in the recovered
matter power spectrum amplitude and dark energy equation of state, for
preliminary Stage III surveys. We demonstrate that these cosmological errors
can be largely removed by marginalising over unknown biases in the assumed weak
lensing redshift distributions, if we assume high quality redshift information
for the galaxy clustering sample. Furthermore the cosmological constraining
power is mostly retained despite removing much of the information on the weak
lensing redshift distribution biases. We show that this comes from
complementary degeneracy directions between cosmic shear and the combination of
galaxy clustering with cross-correlation between shear and galaxy number
density. Finally we examine how the self-calibration performs when the assumed
distributions differ from the true distributions by more than a simple uniform
bias. We find that the effectiveness of this self-calibration method will
depend on the details of a given experiment and the nature of the uncertainties
on the estimated redshift distributions.
