Galaxy-galaxy weak gravitational lensing in $f(R)$ gravity
  We present an analysis of galaxy-galaxy weak gravitational lensing (GGL) in
chameleon $f(R)$ gravity - a leading candidate of non-standard gravity models.
For the analysis we have created mock galaxy catalogues based on dark matter
haloes from two sets of numerical simulations, using a halo occupation
distribution (HOD) prescription which allows a redshift dependence of galaxy
number density. To make a fairer comparison between the $f(R)$ and $\Lambda$CDM
models, their HOD parameters are tuned so that the galaxy two-point correlation
functions in real space (and therefore the projected two-point correlation
functions) match. While the $f(R)$ model predicts an enhancement of the
convergence power spectrum by up to $\sim30\%$ compared to the standard
$\Lambda$CDM model with the same parameters, the maximum enhancement of GGL is
only half as large and less than 5\% on separations above $\sim1$-$2h^{-1}$Mpc,
because the latter is a cross correlation of shear (or matter, which is more
strongly affected by modified gravity) and galaxy (which is weakly affected
given the good match between galaxy auto correlations in the two models)
fields. We also study the possibility of reconstructing the matter power
spectrum by combination of GGL and galaxy clustering in $f(R)$ gravity. We find
that the galaxy-matter cross correlation coefficient remains at unity down to
$\sim2$-$3h^{-1}$Mpc at relevant redshifts even in $f(R)$ gravity, indicating
joint analysis of GGL and galaxy clustering can be a powerful probe of matter
density fluctuations in chameleon gravity. The scale dependence of the model
differences in their predictions of GGL can potentially allow to break the
degeneracy between $f(R)$ gravity and other cosmological parameters such as
$\Omega_m$ and $\sigma_8$.
