Cosmic Concordance and Quintessence

We present a comprehensive study of the observational constraints on spatially flat cosmological models containing a mixture of matter and quintessence --- a time varying, spatially inhomogeneous component of the energy density of the universe with negative pressure. Our study also includes the limiting case of a cosmological constant. We classify the observational constraints by red shift: low red shift constraints include the Hubble parameter, baryon fraction, cluster abundance, the age of the universe, bulk velocity and the shape of the mass power spectrum; intermediate red shift constraints are due to probes of the red shift-luminosity distance based on type 1a supernovae, gravitational lensing, the Lyman-alpha forest, and the evolution of large scale structure; high red shift constraints are based on measurements of the cosmic microwave background temperature anisotropy. Mindful of systematic errors, we adopt a conservative approach in applying these observational constraints. We determine that the range of Quintessence models in which the ratio of the matter density to the critical density is $0.2 \lesssim \Omega_m \lesssim 0.5$ and the equation-of-state is $-1 \le w \lesssim -0.2$ is consistent with the most reliable, current low red shift and microwave background observations at the $2 \sigma$ level. Factoring in the constraint due to the recent measurements of type 1a supernovae, the range for the equation-of-state is reduced to $-1 \le w \lesssim -0.4$. We find that the best-fit and best-motivated models lie in the range $\Omega_m \approx 0.33 \pm 0.05$, with an effective equation-of-state $w \approx -0.65 \pm 0.07$ and $h=0.65 \pm 0.10$, and are consistent with a spectral index $n_s=1$.