Mass bias evolution in tSZ cluster cosmology

Galaxy clusters observed through the thermal Sunyaev-Zeldovich (tSZ) effect are a recent cosmological probe. The precision on the cosmological constraints is affected mainly by the current knowledge of cluster physics, which enters the analysis through the scaling relations. Here we aim to study one of the most important sources of systematic uncertainties, the mass bias, $b$. We have analysed the effects of a mass-redshift dependence, adopting a power-law parametrisation. We applied this parametrisation to the combination of tSZ number counts and power spectrum, finding a hint of redshift dependence that leads to a decreasing value of the mass bias for higher redshift. We tested the robustness of our results for different mass bias calibrations and a discrete redshift dependence. We find our results to be dependent on the clusters sample that we are considering, in particular obtaining an inverse (decreasing) redshift dependence when neglecting $z<0.2$ clusters. We analysed the effects of this parametrisation on the combination of cosmic microwave background (CMB) primary anisotropies and tSZ galaxy clusters. We find a preferred constant value of mass bias, having $(1-b) =0.62 \pm 0.05$. The corresponding value of $b$ is too high with respect to weak lensing and numerical simulations estimations. Therefore we conclude that this mass-redshift parametrisation does not help in solving the remaining discrepancy between CMB and tSZ clusters observations.