  Joint studies of imaging and spectroscopic samples, informed by theory and
simulations, offer the potential for comprehensive tests of the cosmological
model over redshifts z<1.5. Spectroscopic galaxy samples at these redshifts can
be increased beyond the planned Dark Energy Spectroscopic Instrument (DESI)
program by at least an order of magnitude, thus offering significantly more
constraining power for these joint studies. Spectroscopic observations of these
galaxies in the latter half of the 2020's and beyond would leverage the theory
and simulation effort in this regime. In turn, these high density observations
will allow enhanced tests of dark energy, physics beyond the standard model,
and neutrino masses that will greatly exceed what is currently possible. Here,
we present a coordinated program of simulations, theoretical modeling, and
future spectroscopy that would enable precise cosmological studies in the
accelerating epoch where the effects of dark energy are most apparent.
