  Baryon acoustic oscillations (BAOs) and weak lensing (WL) are complementary
probes of cosmology. We explore the distance and growth factor measurements
from photometric BAO and WL techniques and investigate the roles of the
distance and growth factor in constraining dark energy. We find for WL that the
growth factor has a great impact on dark energy constraints but is much less
powerful than the distance. Dark energy constraints from WL are concentrated in
considerably fewer distance eigenmodes than those from BAO, with the largest
contributions from modes that are sensitive to the absolute distance. Both
techniques have some well determined distance eigenmodes that are not very
sensitive to the dark energy equation of state parameters w_0 and w_a,
suggesting that they can accommodate additional parameters for dark energy and
for the control of systematic uncertainties. A joint analysis of BAO and WL is
far more powerful than either technique alone, and the resulting constraints on
the distance and growth factor will be useful for distinguishing dark energy
and modified gravity models. The Large Synoptic Survey Telescope (LSST) will
yield both WL and angular BAO over a sample of several billion galaxies. Joint
LSST BAO and WL can yield 0.5% level precision on ten comoving distances evenly
spaced in log(1+z) between redshift 0.3 and 3 with cosmic microwave background
priors from Planck. In addition, since the angular diameter distance, which
directly affects the observables, is linked to the comoving distance solely by
the curvature radius in the Friedmann-Robertson-Walker metric solution, LSST
can achieve a pure metric constraint of 0.017 on the mean curvature parameter
Omega_k of the universe simultaneously with the constraints on the comoving
distances.
