On problems with cosmography in cosmic dark ages

Quasars show considerable promise as standard candles in a high-redshift window beyond Type Ia supernovae. Recently, Risaliti, Lusso & collaborators [1–3] have succeeded in producing a high redshift Hubble diagram (z≲7) that supports “a trend whereby the Hubble diagram of quasars is well reproduced by the standard flat ΛCDM model up to z∼1.5−2, but strong deviations emerge at higher redshifts”. This conclusion hinges upon a log polynomial expansion for the luminosity distance. In this note, we demonstrate that this expansion (or “improvements” thereof) typically can only be trusted up to z∼1.5−2. As a result, a breakdown in the validity of the expansion may be misinterpreted as a (phantom) deviation from flat ΛCDM. We further illustrate the problem through mock data examples.