Risaliti, Lusso, and collaborators have constructed a high-redshift Hubble diagram of supernovae (SNe), quasars (QSO), and gamma-ray bursts (GRBs) that shows a “$\sim 4\sigma$ tension with the $\mathrm{\Lambda }\mathrm{CDM}$ model” based on a log polynomial cosmographic expansion [1,2]. In this work, we demonstrate that the log polynomial expansion generically fails to recover flat $\mathrm{\Lambda }\mathrm{CDM}$ beyond $z\sim 2$, thus undermining the $\sim 4\sigma$ tension claim. Moreover, through direct fits of both the flat $\mathrm{\Lambda }\mathrm{CDM}$ and the log polynomial model to the $\mathrm{SNe}+\mathrm{QSO}+\mathrm{GRB}$ data set, we confirm that the flat $\mathrm{\Lambda }\mathrm{CDM}$ model is preferred. Ultimately, we trace the tension to the QSO data and show that a best fit of the flat $\mathrm{\Lambda }\mathrm{CDM}$ model to the QSO data leads to a flat $\mathrm{\Lambda }\mathrm{CDM}$ universe with no dark energy within $1\sigma$. This marks an irreconcilable tension between the Risaliti-Lusso QSOs and flat $\mathrm{\Lambda }\mathrm{CDM}$.

• Received 9 September 2020
• Accepted 16 November 2020

DOI:https://doi.org/10.1103/PhysRevD.102.123532