Cosmology from weak lensing alone and implications for the Hubble
  tension
  We investigate the origin of $\Lambda$CDM parameter constraints in weak
lensing, with a focus on the Hubble constant. We explain why current cosmic
shear data are sensitive to the parameter combination $S_8 \propto \sigma_8
\Omega_m^{0.5}$, improving upon previous studies through use of the halo model.
Motivated by the ongoing discrepancy in measurements of the Hubble constant
from high and low redshift, we explain why cosmic shear provides almost no
constraint on $H_0$ by showing how the lensing angular power spectrum depends
on physical length scales in the dark matter distribution. We derive parameter
constraints from galaxy lensing in KiDS and cosmic microwave background weak
lensing from Planck and SPTpol, separately and jointly, showing how
degeneracies between $\sigma_8$ and $\Omega_m$ can be broken. Using lensing and
Big Bang Nucleosynthesis to calibrate the sound horizon measured in projection
by baryon acoustic oscillations gives $H_0 = 67.4 \pm 0.9 \; \mathrm{km} \,
\mathrm{s}^{-1} \, \mathrm{Mpc}^{-1}$, consistent with previous results from
Planck and the Dark Energy Survey. We find that a toy Euclid-like lensing
survey provides only weak constraints on the Hubble constant due to
degeneracies with other parameters that affect the shape of the lensing
correlation functions. If external priors on $n_s$, the baryon density, and the
amplitude of baryon feedback are available then sub-percent $H_0$ constraints
are achievable with forthcoming lensing surveys.
