Is the Hubble diagram of quasars in tension with concordance cosmology?

Recently, Risaliti and Lusso [Nat. Astron. 3, 272 (2019)] reported new measurements of the expansion rate of the Universe by constructing the  Hubble diagram of 1598 quasars in the redshift range $0.5<z<5.5$. It is claimed a $4\sigma$ tension with the standard concordance $\mathrm{\Lambda }\mathrm{CDM}$ concerning both the fractionary matter density ${\mathrm{\Omega }}_{m0}$ and the dark energy equation of state parameter $w_{\mathrm{de}}$ standard values. In this work we promote an independent analysis of the same data set using a model-independent estimator for cosmic acceleration. Our results corroborate that the source of such tension can be related to the ${\mathrm{\Omega }}_{m0}$ value with a reasonable indication of a higher ${\mathrm{\Omega }}_{m0}$ value (${\mathrm{\Omega }}_{m0}\gtrsim 0.4$). On the other hand, we find that the role played by $w_{\mathrm{de}}$ on the claimed tension is weak. We also discuss the use of this estimator as a “quality tool” to test the robustness of Hubble diagrams. We conclude claiming that the quasars data cannot yet be seen as a reliable cosmological tool since they cannot even state the universe experienced an accelerated expansion phase.

Figure 1

Cumulative evidence for the SN PANTHEON (black) sample and QSOsHD (blue).

Figure 2

Magnitude $\mathrm{\Delta }\mu$ averaged over redshift bins of width 0.2 for SN PANTHEON (black) sample and QSOsHD (blue). The inset shows the theoretical evolution of the estimator $\mathrm{\Delta }\mu$ as a function of the redshift. Solid lines adopt ${\mathrm{\Omega }}_{m0}=0.3$ and remain at positive $\mathrm{\Delta }\mu$ values for the interval $0<z<5$. Cosmologies adopting ${\mathrm{\Omega }}_{m0}=0.45$ are plotted in the dashed lines. The dotted line represents the Einstein de-Sitter cosmology ${\mathrm{\Omega }}_{m0}=1$. Both set of curves plotted in the inset assume parameters values in the range $-1.2<w_0<-0.8$ and $-0.2<w_a<+0.2$. The solid and dashed lines shown with the binned data assumed the $\mathrm{\Lambda }\mathrm{CDM}$ model.

Figure 3

Hubble diagram (Distance modulus) as a function of the redshift. Curves and data follow Fig. 2.