Cosmography and flat $\mathrm{\Lambda }$CDM tensions at high redshift

Risaliti, Lusso & collaborators have constructed a high-redshift Hubble diagram of supernovae (SNe); quasars (QSO) and gamma-ray bursts (GRB) that shows a “$\sim 4\sigma$ tension with the $\mathrm{\Lambda }$CDM model” based on a log polynomial cosmographic expansion (Risaliti et.al 2018, Lusso et.al 2019). In this work, we demonstrate that the log polynomial expansion generically fails to recover flat $\mathrm{\Lambda }$CDM beyond $z\sim 2$, thus undermining the $\sim 4 , \sigma$tensionclaim\mathrm{.}Moreover,throughdirectfitsofboththeflat$\Lambda$CDM and the log polynomial model to the SNe+QSO+GRB dataset, we confirm that the flat $\mathrm{\Lambda }$CDM model is preferred. Ultimately, we trace the tension to the QSO data and show that a best-fit of the flat $\mathrm{\Lambda }$CDM model to the QSO data leads to a flat $\mathrm{\Lambda }$CDM Universe with no dark energy within $1\sigma$. This marks an irreconcilable tension between the Risaliti-Lusso QSOs and flat $\mathrm{\Lambda }$CDM.