  Strong gravitational lenses with measured time delays between the multiple
images and models of the lens mass distribution allow a one-step determination
of the time-delay distance, and thus a measure of cosmological parameters. We
present a blind analysis of the gravitational lens RXJ1131-1231 incorporating
(1) the newly measured time delays from COSMOGRAIL, (2) archival HST imaging of
the lens system, (3) a new velocity-dispersion measurement of the lens galaxy
of 323+/-20km/s based on Keck spectroscopy, and (4) a characterization of the
line-of-sight structures via observations of the lens' environment and ray
tracing through the Millennium Simulation. Our blind analysis is designed to
prevent experimenter bias. The joint analysis of the data sets allows a
time-delay distance measurement to 6% precision that takes into account all
known systematic uncertainties. In combination with the WMAP7 data set in flat
wCDM cosmology, our unblinded cosmological constraints for RXJ1131-1231 are:
H_0=80.0+5.8/-5.7km/s/Mpc, OmegaDE=0.79+/-0.03 and w=-1.25+0.17/-0.21. We find
the results to be statistically consistent with those from the analysis of the
gravitational lens B1608+656. The joint constraints from the two lenses and
WMAP7 are H_0=75.2+4.4/-4.2km/s/Mpc, OmegaDE=0.76+0.02/-0.03 and
w=-1.14+0.17/-0.20 in flat wCDM, and H_0=73.1+2.4/-3.6km/s/Mpc,
OmegaL=0.75+0.01/-0.02 and OmegaK=0.003+0.005/-0.006 in open LCDM. Time-delay
lenses constrain especially tightly the Hubble constant (5.7% and 4.0%
respectively in wCDM and open LCDM) and curvature of the universe. They
complement well other cosmological probes, and provide an independent check of
unknown systematics. Our measurement of the Hubble constant is completely
independent of those based on the local distance ladder method, providing an
important consistency check of the standard cosmological model and of general
relativity.
