Observational Constraints on Dark Energy and Cosmic Curvature

Current observational bounds on dark energy depend on assumptions about the curvature of the universe. We present a simple and efficient method for incorporating constraints from CMB anisotropy data, and use it to derive constraints on cosmic curvature and dark energy density as a free function of cosmic time using current data. We show that there are two CMB shift parameters, R=sqrt{\Omega_m H_0^2} r(z_{CMB}) (scaled distance to recombination) and l_a=\pi r(z_{CMB})/r_s(z_{CMB})(angular scale of the sound horizon at recombination), with measured values that are nearly uncorrelated with each other. Allowing nonzero cosmic curvature, the three-year WMAP data give R =1.71 +/- 0.03, l_a =302.5 +/- 1.2, and \Omega_b h^2 = 0.02173 +/- 0.00082, independent of the dark energy model. The corresponding bounds for a flat universe are R =1.70 +/- 0.03, l_a =302.2 +/- 1.2, and \Omega_b h^2 = 0.022 +/- 0.00082. We give the covariance matrix of (R, l_a, \Omega_b h^2) from the three-year WMAP data. We find that (R, l_a, \Omega_b h^2) provide an efficient and intuitive summary of CMB data as far as dark energy constraints are concerned. Using current CMB, SN Ia, and BAO data, we find that dark energy density is consistent with a constant in cosmic time, with marginal deviations from a cosmological constant that may reflect current systematic uncertainties or true evolution in dark energy. A flat universe is allowed by current data: \Omega_k=-0.006_{-0.012}^{+0.013}_{-0.025}^{+0.025} for w_X(z)=const., and \Omega_k=-0.002_{-0.018}^{+0.018}_{-0.032}^{+0.041} for w_X(z)=w_0+w_a(1-a)(68% and 95% C.L.). The bounds on cosmic curvature are less stringent if dark energy density is allowed to be a free function of cosmic time, and are also dependent on the assumption about the early time property of dark energy.