Cosmic concordance and quintessence

We present a comprehensive study of the observational constraints on spatia lly flat cosmological models containing a mixture of matter and quintessenc e-a time-varying, spatially inhomogeneous component of the energy density o f the universe with negative pressure. Our study also includes the limiting case of a cosmological constant. We classify the observational constraints by redshift: low-redshift constraints include the Hubble parameter, baryon fraction, cluster abundance, the age of the universe, bulk velocity and th e shape of the mass power spectrum; intermediate-redshift constraints are d ue to probes of the redshift-luminosity distance based on Type Ia supernova e, gravitational lensing, the Ly alpha forest, and the evolution of large-s cale structure; high-redshift constraints are based on measurements of the cosmic microwave background temperature anisotropy. Mindful of systematic e rrors, we adopt a conservative approach in applying these observational con straints. We determine that the range of quintessence models in which the r atio of the matter density to the critical density is 0.2 less than or simi lar to Omega(m) less than or similar to 0.5, and the effective, density-ave raged equation of state is - 1 less than or equal to w less than or similar to -0.2, is consistent with the most reliable, current low-redshift and mi crowave background observations at the 2 sigma level. Factoring in the cons traint due to the recent measurements of Type Ia supernovae, the range for the equation of state is reduced to -1 less than or equal to w less than or similar to -0.4, where this range represents models consistent with each o bservational constraint at the 2 sigma level or better (concordance analysi s). A combined maximum likelihood analysis suggests a smaller range, - 1 le ss than or equal to w less than or similar to -0.6. We find that the best-f it and best-motivated quintessence models lie near Omega(m) approximate to 0.33, h approximate to 0.65, and spectral index n(s) = 1, with an effective equation of state w approximate to -0.65 for "tracker" quintessence and w = -1 for "creeper" quintessence.