Halo mass and weak galaxy-galaxy lensing profiles in rescaled
  cosmological $N$-body simulations
  We investigate 3D density and weak lensing profiles of dark matter haloes
predicted by a cosmology-rescaling algorithm for $N$-body simulations. We
extend the rescaling method of Angulo & White (2010) and Angulo & Hilbert
(2015) to improve its performance on intra-halo scales by using models for the
concentration-mass-redshift relation based on excursion set theory. The
accuracy of the method is tested with numerical simulations carried out with
different cosmological parameters. We find that predictions for median density
profiles are more accurate than $\sim 5\,\%$ for haloes with masses of
$10^{12.0} - 10^{14.5} h^{-1}\,M_{\odot}$ for radii $0.05 < r/r_{200\text{m}} <
0.5$, and for cosmologies with $\Omega_\text{m} \in [0.15,\,0.40]$ and
$\sigma_8 \in [0.6,\,1.0]$. For larger radii, $0.5 < r/r_{200\text{m}} < 5$,
the accuracy degrades to $\sim20\,\%$, due to inaccurate modelling of the
cosmological and redshift dependence of the splashback radius. For changes in
cosmology allowed by current data, the residuals decrease to $\lesssim2\,\%$ up
to scales twice the virial radius. We illustrate the usefulness of the method
by estimating the mean halo mass of a mock galaxy group sample. We find that
the algorithm's accuracy is sufficient for current data. Improvements in the
algorithm, particularly in the modelling of baryons, are likely required for
interpreting future (dark energy task force stage IV) experiments.
