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, $z=0.2$, $z=0.3$, and $z=0.5$. The number of objects is $12910$, $42215$, and $11816$, respectively. We detect the peak of baryon acoustic oscillations for all the three samples. The derived distance constraints are: $r_s/D_V(z=0.2)=0.18 pm 0.01$, $r_s/D_V(z=0.3)=0.124 pm 0.004$ and $r_s/D_V(z=0.5)=0.080 pm 0.002$. Combining these measurements, we obtain robust constraints on cosmological parameters. Our results are in agreement with the standard $Lambda$ cold dark matter model. Specifically, we constrain the Hubble constant in a $Lambda$CDM model, $H_0 = 64_{-9}^{+14} , mathrm{km} , mathrm{s}^{-1}mathrm{Mpc}^{-1}$, the density of curvature energy, in the $oLambda$CDM context, $Omega_K = -0.015_{-0.36}^{+0.34}$, and finally the parameter of the dark energy equation of state in the $ow$CDM case, $w = -1.01_{-0.44}^{+0.44}$. This is the first time the distance-redshift relation has been constrained using only the peak of baryon acoustic oscillations of galaxy clusters.
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