  The accurate determination of the galaxy cluster mass-observable relations is
one of the major challenge of modern astrophysics and cosmology. We present a
new statistical methodology to constrain the evolution of the mass-observable
relations. Instead of measuring individual mass of galaxy clusters, we only
consider large scale homogeneity of the Universe. In this case, we expect the
present galaxy cluster mass function to be the same everywhere in the Universe.
Using relative abundance matching, we contraint the relation between the
richness, $\lambda(z)$, and the expected present mass, $M(t_0)$, of galaxy
clusters. We apply this approach to the redMaPPer galaxy cluster catalogue in
10 redshift bins from $z=0.1$ to $0.6$. We found that the $\lambda(z)$-$M(t_0)$
relation is not evolving from $z=0.1$ to $0.4$, whereas it starts to
significantly evolve at higher redshift. This results implies that the
redMaPPer richness appears to be a better proxy for the expected present-day
galaxy cluster mass than for the mass at the observational redshift. Assuming
cosmology and galaxy cluster mass accretion history, it is possible to convert
$M(t_0)$ to the mass at the galaxy cluster redshift $M(t_z)$. We found a
significant evolution of the $\lambda(z)$-$M(t_z)$ over all the covered
redshift range. Consequently, we provide a new redshift-dependent richness-mass
relation for the redMaPPer galaxy cluster catalogue. This results demonstrates
the efficiency of this new methodology to probe the evolution of scaling
relations compared to individual galaxy cluster mass estimation.
