Results from a fit of a w₀w_aCDM model to our Hubble diagram of supernovae and quasars in four different cases. Top left: whole quasar sample, with the slope of the L_X − L_UV relation as a free parameter; top right: quasars at z >  0.7 with a fixed L_X − L_UV slope, γ = 0.59, that is the average value from the fit of the relation in narrow redshift intervals, as shown in Sect. 8; bottom panels: results for two sub-samples with Γ_X <  2.2 and Γ_X >  2.2. Contours are at the 1σ, 2σ, and 3σ confidence levels. The green contours refer to the CMB results from Planck (Planck Collaboration VI 2020). The orange, red, and brown contours are obtained by adding the constraints from the Hubble diagram of supernovae and quasars.