Cosmography and flat <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi><mml:mi>CDM</mml:mi></mml:mrow></mml:math> tensions at high redshift
Tao Yang, Aritra Banerjee, Eoin Ó Colgáin
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 ``$\ensuremath{\sim}4\ensuremath{\sigma}$ tension with the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ 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 $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ beyond $z\ensuremath{\sim}2$, thus undermining the $\ensuremath{\sim}4\ensuremath{\sigma}$ tension claim. Moreover, through direct fits of both the flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ and the log polynomial model to the $\mathrm{SNe}+\mathrm{QSO}+\mathrm{GRB}$ data set, we confirm that the flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model is preferred. Ultimately, we trace the tension to the QSO data and show that a best fit of the flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model to the QSO data leads to a flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ universe with no dark energy within $1\ensuremath{\sigma}$. This marks an irreconcilable tension between the Risaliti-Lusso QSOs and flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$.