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. Low red shift constraints include the Hubble parameter, baryon fraction, cluster abundance, age of the universe, bulk velocity and shape of the mass power spectrum; intermediate red shift constraints are due to type 1a supernovae, gravitational lensing, the Ly-a forest, and the evolution of large scale structure; high red shift constraints are based on cosmic microwave background temperature anisotropy. Mindful of systematic errors, we adopt a conservative approach in applying these constraints. We determine that quintessence models in which the matter density parameter is $0.2 \ls \Omega_m \ls 0.5$ and the effective, density-averaged equation of state is $-1 \le w \ls -0.2$, are consistent with the most reliable, current low red shift and CMB observations at the $2\sigma$ level. Factoring in the constraint due to type 1a SNe, the range for the equation of state is reduced to $-1 \le w \ls -0.4$, where this range represents models consistent with each observational constraint at the 2$\sigma$ level or better (concordance analysis). A combined maximum likelihood analysis suggests a smaller range, $-1 \le w \ls -0.6$. We find that the best-fit and best-motivated quintessence models lie near $\Omega_m \approx 0.33$, $h \approx 0.65$, and spectral index $n_s=1$, with an effective equation of state $w \approx -0.65$ for ``tracker'' quintessence and $w=-1$ for ``creeper'' quintessence. (abstract shortened)