Can the Distance‒Redshift Relation be Determined from Correlations between Luminosities?

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 wave-band 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 independently of the cosmological model and measured fluxes and redshifts, for example, based on sound theoretical models or unrelated observations. In particular, we show that if the correlation is determined empirically for two luminosities obtained from fluxes and redshifts, then the method suffers from circularity. In the case where the observed correlation between fluxes in very narrow redshift bins is used as a proxy for the luminosity correlation, 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.

A Bias-free Cosmological Analysis with Quasars Alleviating H 0 Tension

“…The latter technique has recently been applied to GRBs (Dainotti et al 2023), but this is the first time in the literature that it has been used for QSOs. This study also addresses some previous criticisms concerning the application of the X-UV relation in cosmology (e.g., Petrosian et al 2022). All of these approaches have also been explored using both noncalibrated QSOs combined with SNe Ia and QSOs alone calibrated with SNe Ia.…”

“…Recent studies have investigated the reliability of the application of the X-UV relation in cosmology. In Petrosian et al (2022), the authors argued that the RL procedure is circular. In this work, we completely overcome, for the first time in the literature on QSOs, the circularity problem while also accounting for the correction for evolution in redshift of luminosities.…”

Reducing the Uncertainty on the Hubble Constant up to 35% with an Improved Statistical Analysis: Different Best-fit Likelihoods for Type Ia Supernovae, Baryon Acoustic Oscillations, Quasars, and Gamma-Ray Bursts

“…X,UV , where K = 1 (Lusso et al 2020) since the QSO spectral index is assumed to be 1. One can argue (see Petrosian et al 2022) that given that the X-UV relation is based on both luminosities, the relation is independent of cosmology. However, this is not the case because if we subtract from both members of Equation (10) the distance luminosity, d l (Equation ( 3)), the parameter n 1 still should be subtracted by d l , and thus (unless g 1 = 1) the parameters g 1 and n 1 change when varying the cosmological parameters.…”

$H_0=69.8\pm1.3$ $\rm{km \ s^{-1} \ Mpc^{-1}}$, $Ω_{m0}=0.288\pm0.017$, and other constraints from lower-redshift, non-CMB and non-distance-ladder, expansion-rate data

“…In our analyses here we also exclude RM Hβ QSO data that probe to z ∼ 0.9, [22,23,44], because the resulting cosmological parameter constraints are in ∼ 2σ tension with those from more established probes. QSO flux observations that reach to z ∼ 7.5 have been studied, [45][46][47][48][49][50][51][52][53][54][55], however, we also exclude these QSOs from our analyses here since the latest QSO flux compilation, [50], is not standardizable, [51,52,56,57].…”