Impact of thawing parameters in the scaling relations. XXL ASpiX (base) refers to the results presented in Sect. 4.1 (two free scaling parameters); XXL-HSC ASpiX contours are the results following the methodology presented in Sect. 5 (six free cosmology-dependent scaling parameters); simple dark blue contours, same as XXL-HSC but the priors of the scaling coefficients are fixed to the indicated cosmology. We can see that, in this case, the results in Ω_m − σ₈ are shifted (lower Ω_m and higher σ₈) because of the fact that the scaling relation priors do not depend on the cosmology and then introduce a bias in the analysis.