  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
$o\Lambda$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.
