  The exquisite measurements of the cosmic microwave background (CMB)
fluctuations by Planck allows us to tightly constrain the amplitude of matter
fluctuations at redshift $\sim 1100$ in the $\Lambda$-cold dark matter
($\Lambda$CDM) model. This amplitude can be extrapolated to the present epoch,
yielding constraints on the value of the $\sigma_8$ parameter. On the other
hand the abundance of Sunyaev-Zeldovich (SZ) clusters detected by Planck, with
masses inferred by using hydrostatic equilibrium estimates, leads to a
significantly lower value of the same parameter. This discrepancy is often
dubbed the "$\sigma_8$ tension" in the literature and is sometimes regarded as
a possible sign of new physics. Here, we examine a direct determination of
$\sigma_8$ at the present epoch in $\Lambda$CDM, and thereby the cluster mass
calibrations using cosmological data at low redshift, namely the measurements
of $f\sigma_8$ from the analysis of the completed Sloan Digital Sky Survey
(SDSS): we combine redshift-space distortions measurements with Planck CMB
constraints, X-ray, and SZ cluster counts within the $\Lambda$CDM framework,
but leaving the present day amplitude of matter fluctuations as an independent
parameter (i.e. no extrapolation is made from high-redshift CMB constraints).
The calibration of X-ray and SZ masses are therefore left as free parameters
throughout the whole analysis. Our study yields tight constraints on the
aforementioned calibrations, with values entirely consistent with results
obtained from the full combination of CMB and cluster data only. Such agreement
suggests an absence of tension in the $\Lambda$CDM model between CMB-based
estimates of $\sigma_8$ and constraints from low-redshift on $f\sigma_8$ but
indicates a tension with the standard calibration of clusters masses.
