Cosmography and flat Λ⁢CDM tensions at high redshift

Abstract

Risaliti, Lusso, and collaborators have constructed a high-redshift Hubble diagram of supernovae (SNe), quasars (QSO), and gamma-ray bursts (GRBs) that shows a “∼4⁢𝜎 tension with the Λ⁢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 Λ⁢CDM beyond 𝑧∼2, thus undermining the ∼4⁢𝜎 tension claim. Moreover, through direct fits of both the flat Λ⁢CDM and the log polynomial model to the SNe+QSO+GRB data set, we confirm that the flat Λ⁢CDM model is preferred. Ultimately, we trace the tension to the QSO data and show that a best fit of the flat Λ⁢CDM model to the QSO data leads to a flat Λ⁢CDM universe with no dark energy within 1⁢𝜎. This marks an irreconcilable tension between the Risaliti-Lusso QSOs and flat Λ⁢CDM.