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 (1) new, deep Hubble Space Telescope (HST) observations, (2) a new velocity-dispersion measurement of 260 +/- 15 km s(-1) for the primary lens galaxy, and (3) an updated study of the lens' environment. Our analysis of the HST images takes into account the extended source surface brightness, and the dust extinction and optical emission by the interacting lens galaxies. 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 k(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 k(ext): 0.10(-0.05)(+0.08). This latter distribution dominates the final uncertainty on H(0). Fixing the cosmological parameters at Omega(m) = 0.3, Omega(A) = 0.7, and w = -1 in order to compare with previous work on this system, we find H(0) = 70.6(-3.1)(+3.1) km s(-1) Mpc(-1). The new data provide an increase in precision of more than a factor of 2, even including the marginalization over k(ext). Relaxing the prior probability density function for the cosmological parameters to that derived from the Wilkinson Microwave Anisotropy Probe (WMAP) five-year data set, we find that the B1608+656 data set breaks the degeneracy between Omega(m) and Omega(A) at w = -1 and 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(-5.0)(+4.9) km s(-1) Mpc(-1) and w = -0.94(-0.19)(+0.17) (68% CL), suggesting that the observations of B1608+656 constrain w as tightly as the current Baryon Acoustic Oscillation data do.