The Age of the Universe and the Cosmological Constant Determined from Cosmic Microwave Background Anisotropy Measurements

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Abstract
If Omega_tot = 1 and structure formed from adiabatic initial conditions then the age of the Universe, as constrained by measurements of the cosmic microwave background (CMB), is t_0=14.0 +/- 0.5 Gyr. The uncertainty is surprisingly small given that CMB data alone constrain neither h nor Omega_Lambda significantly. It is due to the tight (and accidental) correlation, in these models, of the age with the angle subtended by the sound horizon on the last--scattering surface and thus with the well-determined acoustic peak locations. If we assume either the HST Key Project result h = 0.72 pm .08 or simply that h > 0.55, we find Omega_Lambda > 0.4 at 95% confidence--another argument for dark energy, independent of supernovae observations. Our analysis is greatly simplified by the Monte Carlo Markov chain approach to Bayesian inference combined with a fast method for calculating angular power spectra.