The Impact of Magnification and Size Bias on Weak Lensing Power Spectrum
  and Peak Statistics
  The weak lensing power spectrum is a powerful tool to probe cosmological
parameters. Additionally, lensing peak counts contain cosmological information
beyond the power spectrum. Both of these statistics can be affected by the
preferential selection of source galaxies in patches of the sky with high
magnification, as well as by the dilution in the source galaxy surface density
in such regions. If not accounted for, these biases introduce systematic errors
for cosmological measurements. Here we quantify these systematic errors, using
convergence maps from a suite of ray-tracing N-body simulations. At the cut-off
magnitude m of on-going and planned major weak lensing surveys, the logarithmic
slope of the cumulative number counts s = dlog[n(>m)]/dlog(m) is in the range
0.1 < s < 0.5. At s = 0.2, expected in the I band for LSST, the inferred values
of Omega_m, w and sigma_8 are biased by many sigma (where sigma denotes the
marginalized error) and therefore the biases will need to be carefully modeled.
We also find that the parameters are biased differently in the (Omega_m, w,
sigma_8) parameter space when the power spectrum and when the peak counts are
used. In particular, w derived from the power spectrum is less affected than w
derived from peak counts, while the opposite is true for the best-constrained
combination of [sigma_8 Omega_m^gamma] (with gamma=0.62 from the power spectrum
and gamma = 0.48 from peak counts). This suggests that the combination of the
power spectrum and peak counts can help mitigate the impact of magnification
and size biases.
