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 redshift: low-redshift 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-redshift constraints are due to probes of the redshift-luminosity distance based on Type Ia supernovae, gravitational lensing, the Lyα forest, and the evolution of large-scale structure; high-redshift 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 Ωm 0.5, and the effective, density-averaged equation of state is -1 ≤ w -0.2, is consistent with the most reliable, current low-redshift and microwave background observations at the 2 σ level. Factoring in the constraint due to the recent measurements of Type Ia supernovae, the range for the equation of state is reduced to -1 ≤ w -0.4, where this range represents models consistent with each observational constraint at the 2 σ level or better (concordance analysis). A combined maximum likelihood analysis suggests a smaller range, -1 ≤ w -0.6. We find that the best-fit and best-motivated quintessence models lie near Ωm ≈ 0.33, h ≈ 0.65, and spectral index ns = 1, with an effective equation of state w ≈ -0.65 for "tracker" quintessence and w = -1 for "creeper" quintessence.
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