On Problems with Cosmography in Cosmic Dark Ages

TL;DR

This paper critiques the use of log polynomial expansions for high-redshift quasar data, showing they are only reliable up to z~1.5-2 and may falsely suggest deviations from the standard cosmological model.

Contribution

It demonstrates that common luminosity distance expansions are limited in redshift range, potentially leading to misinterpretations of cosmological deviations.

Findings

Expansion validity limited to z~1.5-2

Misinterpretation of breakdown as deviations from ΛCDM

Mock data illustrates the problem

Abstract

Quasars show considerable promise as standard candles in a high-redshift window beyond Type Ia supernovae. Recently, Risaliti, Lusso \& collaborators \cite{Risaliti:2018reu, Lusso:2019akb, Lusso:2020pdb} have succeeded in producing a high redshift Hubble diagram ($ z \lesssim 7$) that supports "a trend whereby the Hubble diagram of quasars is well reproduced by the standard flat $\Lambda$CDM model up to $z \sim 1.5-2$, 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 $z \sim 1.5-2$. As a result, a breakdown in the validity of the expansion may be misinterpreted as a (phantom) deviation from flat $\Lambda$CDM. We further illustrate the problem through mock data examples.