Dissecting the Gravitational Lens B1608+656. II. Precision Measurements of the Hubble Constant, Spatial Curvature, and the Dark Energy Equation of State

Strong gravitational lens systems with measured time delays between the multiple images provide a method for measuring the "time-delay distance" to the lens, and thus the Hubble constant. We present a Bayesian analysis of the strong gravitational lens system B1608+656, incorporating (i) new, deep Hubble Space Telescope (HST) observations, (ii) a new velocity dispersion measurement of 260+/-15 km/s for the primary lens galaxy, and (iii) an updated study of the lens' environment. When modeling the stellar dynamics of the primary lens galaxy, the lensing effect, and the environment of the lens, we explicitly include the total mass distribution profile logarithmic slope gamma' and the external convergence kappa_ext; we marginalize over these parameters, assigning well-motivated priors for them, and so turn the major systematic errors into statistical ones. The HST images provide one such prior, constraining the lens mass density profile logarithmic slope to be gamma'=2.08+/-0.03; a combination of numerical simulations and photometric observations of the B1608+656 field provides an estimate of the prior for kappa_ext: 0.10 +0.08/-0.05. This latter distribution dominates the final uncertainty on H_0. Compared with previous work on this system, the new data provide an increase in precision of more than a factor of two. In combination with the WMAP 5-year data set, we find that the B1608+656 data set constrains the curvature parameter to be -0.031 < Omega_k < 0.009 (95% CL), a level of precision comparable to that afforded by the current Type Ia SNe sample. Asserting a flat spatial geometry, we find that, in combination with WMAP, H_0 = 69.7 +4.9/-5.0 km/s/Mpc and w=-0.94 +0.17/-0.19 (68% CL), suggesting that the observations of B1608+656 constrain w as tightly as do the current Baryon Acoustic Oscillation data. (abridged)