Comment on "Model Independent Evidence for Dark Energy Evolution from Baryon Acoustic Oscillations"

In a recent paper (astro-ph.CO/1406.2209), Sahni et al. showed, by employing the new diagnostic Omh, that the recent observations of Baryon Acoustic Oscillations (BAO) in SDSS DR9 and DR11 have considerable tension with the Planck+WP measurements in the framework of the standard ΛCDM model. In this comment, with the H(z) dataset used in astro-ph.CO/1406.2209 and the Planck distance priors dataset, we perform different joint data analysis to study this tension. We find that the main contribution to the tension comes from the Hubble parameter at redshift of z = 2.34, and that there is no visible tension once the Planck distance priors are used. A recent paper [1] tests the cosmological constant hypothesis via employing the evolution of H(z) according to the recent observations of BAO’s in SDSS DR9[2] and DR11[3]. The authors point out that the measurements of H(z) parameter at different redshifts are statistically independent, thus are suitable for testing the cosmological constant hypothesis. By adopting an improved version of the Om diagnostic,they find that there is considerable tension with the Planck+WP measurements in the framework of the standard ΛCDM model. If dark energy is a constant, then Omh2 is independent of the redshift. However, they find that Om(z = 2.34)h2 = 0.122 ± 0.01, while the Planck result is Omh2 = 0.1426 ± 0.0025. Therefore, the ΛCDM ∗asiahu@itp.ac. cn †mli@itp.ac. cn ‡zhangzhh@itp.ac. cn 1 ar X iv :1 40 6. 76 95 v1 [ as tr oph . C O ] 3 0 Ju n 20 14 Table 1: Fitting results of the ΛCDM model. Dataset SDSS Planck SDSS(lowz) + Planck SDSS + Planck Ωmh 2 0.122 ± 0.009a 0.141 ± 0.003 0.141 ± 0.002 0.140 ± 0.002 χmin 0.003 0.001 0.404 4.379 a We list the best-fits and 68% CL limits. Table 2: Fitting results of the wCDM model. Dataset SDSS SDSS + Planck Ωmh 2 0.121 −0.017 0.141 +0.002 −0.003 w −0.984 −0.257 −1.093 +0.106 −0.096 χmin 0.0002 3.631 model is in conflict with the Hubble parameter measurement at redshift z = 2.34, at the level of two standard deviation. In this comment, we investigate this tension through data analysis instead of theOmh2 diagnostic. For comparison, we use the sameH(z) dataset of[1], including H(z = 0) = 70.6±3.2 km/sec/Mpc, H(z = 0.57) = 92.4±4.5 km/sec/Mpc and the new H(z) data of SDSS DR11, which gives H(z) = 222 ± 7 km/sec/Mpc at z = 2.34. We shall perform two different kinds of analysis: the first includes the Hubble parameter at three different redshifts, while the second employs both the Hubble parameter and the Planck “distance priors”[4]. The distance priors are treated as an efficient summary of CMB data, including the baryon component ωb ≡ Ωbh, the “acoustic scale” la ≡ πr(z∗)/rs(z∗), and the “shift parameter” R ≡ √ ΩmH 0 r(z∗)( see [4] for more details). In the following context, we will use “SDSS”,“SDSS(lowz)” and “Planck” to represent the whole three H(z) data points, the two H(z) data points at z = 0 and 0.57 and the Planck distance priors dataset respectively. With these datasets, we perform χ2 analysis and explore the parameter space using Markov Chain Monte Carlo (MCMC) algorithm by modifying the CosmoMC package [5]. For the ΛCDM model, we do χ2 analysis with datasets of SDSS, Planck, SDSS(lowz) +Planck and SDSS +Planck, respectively. For comparison, we also do joint analysis in the wCDM model. The fitting results of the parameter constraints (the best-fits and 68% CL limits) and corresponding χmin’s are summarized in Table 1 and Table 2. Paper [1] shows that the estimation of the new diagnostic Omh2 from SDSS DR9 and DR11 data gives Ωmh 2 ≈ 0.122 ± 0.01, having tension with the value Ω0mh 2 = 0.1426±0.0025 determined for ΛCDM from Planck+WP