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

If Ωtot = 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 t0 = 14.0 ± 0.5 Gyr. The uncertainty is surprisingly small given that CMB data alone do not significantly constrain either h or ΩΛ. This small uncertainty is due to the tight (and accidental) correlation in flat adiabatic 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 Hubble Space Telescope Key Project result h = 0.72 ± 0.08 or simply that h > 0.55, we find ΩΛ > 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.