  A space-based galaxy redshift survey would have enormous power in
constraining dark energy and testing general relativity, provided that its
parameters are suitably optimized. We study viable space-based galaxy redshift
surveys, exploring the dependence of the Dark Energy Task Force (DETF)
figure-of-merit (FoM) on redshift accuracy, redshift range, survey area, target
selection, and forecast method. Fitting formulae are provided for convenience.
We also consider the dependence on the information used: the full galaxy power
spectrum P(k, P(k) marginalized over its shape, or just the Baryon Acoustic
Oscillations (BAO). We find that the inclusion of growth rate information
(extracted using redshift space distortion and galaxy clustering amplitude
measurements) leads to a factor of ~ 3 improvement in the FoM, assuming general
relativity is not modified. This inclusion partially compensates for the loss
of information when only the BAO are used to give geometrical constraints,
rather than using the full P(k) as a standard ruler. We find that a space-based
galaxy redshift survey covering ~20,000 deg^2 over 0.5< z < 2 with
\sigma_z/(1+z)<= 0.001 exploits a redshift range that is only easily accessible
from space, extends to sufficiently low redshifts to allow both a vast 3-D map
of the universe using a single tracer population, and overlaps with
ground-based surveys to enable robust modeling of systematic effects. We argue
that these parameters are close to their optimal values given current
instrumental and practical constraints.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology