Comparison of standard ruler and standard candle constraints on dark energy models

We compare the dark energy model constraints obtained by using recent standard ruler data (baryon acoustic oscillations (BAO) at z = 0.2 and 0.35 and cosmic microwave background (CMB) shift parameters R and l_a) with the corresponding constraints obtained by using recent type Ia supernovae (SnIa) standard candle data (ESSENCE+SNLS+HST from astro-ph/0701510). We find that, even though both classes of data are consistent with ΛCDM (CDM: cold dark matter) at the 2σ level, there is a systematic difference between the two classes of data. In particular, we find that for practically all values of the parameters (Ω_0m,Ω_b) in the 2σ range of the three-year WMAP data (WMAP3) best fit, ΛCDM is significantly more consistent with the SnIa data than with the CMB+BAO data. For example for (Ω_0m,Ω_b) = (0.24,0.042) corresponding to the best fit values of WMAP3, the dark energy equation of state parameterization w(z) = w₀+w₁(z/1+z) best fit is at a 0.5σ distance from ΛCDM (w₀ = -1,w₁ = 0) using the SnIa data and 1.7σ away from ΛCDM using the CMB+BAO data. There is a similar trend in the earlier data (SNLS versus CMB+BAO at z = 0.35). This trend is such that the standard ruler CMB+BAO data show a mild preference for crossing of the phantom divide line w = -1, while the recent SnIa data favor ΛCDM. Despite this mild difference in trends, we find no statistically significant evidence for violation of the cosmic distance duality relation \eta \equiv {d_L(z)}/{d_A(z)

(1+z)^2}=1 . For example, using a prior of Ω_0m = 0.24, we find η = 0.95 ± 0.025 in the redshift range 0<z<2, which is consistent with distance duality at the 2σ level.