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 .