Can the Distance-Redshift Relation Be Determined from Correlations Between Luminosities?

TL;DR

This paper critically examines whether correlations between luminosities can independently determine the cosmic distance-redshift relation, concluding that such methods are circular or tautological unless based on independent, model-free correlations.

Contribution

It clarifies the conditions under which luminosity correlations can inform cosmological distances, highlighting the pitfalls of empirical correlations derived from fluxes and redshifts.

Findings

Empirical luminosity correlations suffer from circularity when used to determine cosmology.

Using flux correlations in narrow redshift bins leads to tautologies, providing no new distance information.

Numerical analysis with quasar data demonstrates the incomplete treatment of correlations causes these issues.

Abstract

We explore whether an independent determination of the distance-redshift relation, and hence cosmological model parameters, can be obtained from the apparent correlations between two different waveband luminosities or fluxes, as has been claimed in recent works using the X-ray and ultraviolet luminosities and fluxes of quasars. We show that such an independent determination is possible only if the correlation between luminosities is obtained independent of the cosmological model, and measured fluxes and redshifts; for example, being based on sound theoretical models or unrelated observations. In particular, we show that if the correlation is determined empirically from two luminosities obtained from fluxes and redshifts, then the method suffers from circularity. In case, as claimed in recent works, the observed correlation between fluxes in very narrow redshift bins are used as proxy for the luminosity correlation, then we show that one is dealing with a pure tautology with no information on distances and cosmological model. We argue that the problem arises because of the incomplete treatment of the correlation and we use numerical methods with a joint X-ray and ultraviolet quasar data set to demonstrate this shortcoming.