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

Understand

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.