Observational constraints on dark energy and cosmic curvature

Abstract

Current observational bounds on dark energy depend on our assumptions about the curvature of the universe. We present a simple and efficient method for incorporating constraints from Cosmic Microwave Background (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 CMB, Type Ia supernova (SN Ia), and baryon acoustic oscillation (BAO) data.We show that there are two CMB shift parameters, R ≡ ΩmH 2 0 r(zCMB) (the scaled distance to recombination) and la ≡ πr(zCMB)/rs(zCMB) (the 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, la = 302.5 ± 1.2, and Ω 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, la = 302.2 ± 1.2, and Ω b h 2 = 0.022 ± 0.00082. We give the covariance matrix of (R, la, Ω b h 2 ) from the three-year WMAP data. We find that (R, la, Ω b h 2 ) provide an efficient and intuitive summary of CMB data as far as dark energy constraints are concerned.Assuming the HST prior of H0 = 72 ± 8 (km/s)Mpc −1 , using 182 SNe Ia (from the HST/GOODS program, the first year Supernova Legacy Survey, and nearby SN Ia surveys), (R, la, Ω b h 2 ) from WMAP three year data, and SDSS measurement of the baryon acoustic oscillation scale, 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: Ω k = −0.006 +0.013 −0.012 +0.025 −0.025 for assuming that the dark energy equation of state wX (z) is constant, and Ω k = −0.002 +0.018 −0.018 +0.041 −0.032 for wX (z) = w0 + wa(1 − a) (68% and 95% confidence levels). 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. We demonstrate this by studying two examples. Significant improvement in dark energy and cosmic curvature constraints is expected as a result of future dark energy and CMB experiments.

Comparison of dark energy models: A perspective from the latest observational data

“…Actually, in Ref. [42], Wang and Mukherjee have argued that because of calibration uncertainties, SN data need to be marginalized over h if SN data are combined with data that are sensitive to the value of h. Our results further confirm this opinion.…”

Dark Energy

“…Therefore, most researchers have chosen to study dark energy by constraining w from observations. However, in a series of works [515,719,720,721,722,723,724], Wang and collaborators argued that, due to the smearing effect [712] arising from the multiple integrals relating w(z) to the luminosity distance of SN d L (z), it is difficult to constrain w using the SN data [711]. On the contrary, since using the dark energy density ρ de can minimize the smearing effect by removing one integral, ρ de can be constrained more tightly than w given the same observational data (see Fig.…”

Curvature versus distances: Testing the FLRW cosmology

“…Similarly, ref. [19] has used the SnIa of [36] and the measurement of H 0 of [35] or of [37], in combination with H(z) measurements coming either from passively evolving galaxies [29,33], or from BAO data [38], together with cosmic microwave background data [39]. No evidence for deviations from FLRW nor from flatness was found.…”