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 ∼< Ωm ∼< 0.5 and the effective, density-averaged equation-of-state is −1 ≤ w ∼< −0.2, are consistent with the most reliable, current low red shift and microwave background observations at the 2σ 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 ≤ w ∼< −0.4, where this range represents models consistent with each observational constraint at the 2σ 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.