Measuring the distance-redshift relation with the baryon acoustic oscillations of galaxy clusters

We analyse the largest spectroscopic samples of galaxy clusters to date, and provide observational constraints on the distance-redshift relation from baryon acoustic oscillations. The cluster samples considered in this work have been extracted from the Sloan Digital Sky Survey at three median redshifts, z = 0.2, 0.3 and 0.5. The number of objects is 12 910, 42 215 and 11 816, respectively. We detect the peak of baryon acoustic oscillations for all the three samples. The derived distance constraints are rs/DV(z = 0.2) = 0.18 \ub1 0.01, rs/DV(z = 0.3) = 0.124 \ub1 0.004 and rs/DV(z = 0.5) = 0.080 \ub1 0.002. Combining these measurements with the sound horizon scale measured from the cosmic microwave background, we obtain robust constraints on cosmological parameters. Our results are in agreement with the standard \u39b cold dark matter (\u39bCDM) model. Specifically, we constrain the Hubble constant in a \u39bCDM model, H0 = 64-8+17 km s-1 Mpc-1, the density of curvature energy, in the o\u39bCDM context, \u3a9K = -0.01-0.33+0.34, and finally the parameter of the dark energy equation of state in the wCDM case, w = -1.06-0.52+0.49. This is the first time the distance-redshift relation has been constrained using only the peak of baryon acoustic oscillations of galaxy clusters