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

Abstract

Cosmological models and their parameters are widely debated because of theoretical and observational mismatches of the standard cosmological model, especially the current discrepancy between the value of the Hubble constant, H 0, obtained by Type Ia supernovae (SNe Ia), and the cosmic microwave background radiation (CMB). Thus, considering high-redshift probes like quasars (QSOs), having intermediate redshifts between SNe Ia and CMB, is a necessary step. In this work, we use SNe Ia and the most updated QSO sample, reaching redshifts up to z ∼ 7.5, applying the Risaliti–Lusso QSO relation based on a nonlinear relation between ultraviolet and X-ray luminosities. We consider this relation both in its original form and corrected for selection biases and evolution in redshift through a reliable statistical method also accounting for the circularity problem. We also explore two approaches: with and without calibration on SNe Ia. We then investigate flat and nonflat standard cosmological models and a flat wCDM model, with a constant dark energy equation-of-state parameter w. Remarkably, when correcting for the evolution as a function of cosmology, we obtain closed constraints on Ω M using only noncalibrated QSOs. We find that considering noncalibrated QSOs combined with SNe Ia and accounting for the same correction, our results are compatible with a flat ΛCDM model with Ω M = 0.3 and H 0 = 70 km s−1 Mpc−1. Intriguingly, the H 0 values obtained are placed halfway between the one from SNe Ia and CMB, paving the way for new insights into the H 0 tension.

Quasars: Standard Candles up to z = 7.5 with the Precision of Supernovae Ia

“…We clarify that previous works have not considered selection biases and redshift evolution with the exception of our works in the literature (Dainotti et al 2022a;Bargiacchi et al 2023;Lenart et al 2023). Since quasars are high-redshift sources, we need to account for selection biases and redshift evolution effects.…”

“…We note here some differences between our sample and the samples used in previous works. Here, we study this final sample of 2421 sources without any additional selection, such as the cut at redshift z = 0.7 previously used in some works (Lusso et al 2020;Bargiacchi et al 2022), to avoid any possible induced bias due to the reduction of the redshift sample (Dainotti et al 2022a;Lenart et al 2023).…”

“…To correct for these effects, we have applied the statistical Efron & Petrosian method (Efron & Petrosian 1992), assuming that the luminosities evolve with redshift as (1 + z) k . This method has already been employed for GRBs (Dainotti et al 2013(Dainotti et al , 2015(Dainotti et al , 2017(Dainotti et al , 2021a(Dainotti et al , 2023a and quasars (Dainotti et al 2022a;Lenart et al 2023). The choice of a more complex function for redshift evolution would not affect the results (Singal et al 2011;Dainotti et al 2021cDainotti et al , 2022a.…”

“…The values of k UV and k X used to determine ¢ L UV and ¢ L X are, respectively, k UV = 4.36 ± 0.08 and k X = 3.36 ± 0.07 (Dainotti et al 2022a), which have been obtained within a flat ΛCDM model with Ω M = 0.3 and H 0 = 70 km s −1 Mpc −1 , consistent with our assumption. The evolutionary parameter k depends on Ω M , but not on H 0 (Dainotti et al 2022a(Dainotti et al , 2023aLenart et al 2023). Thus, when we change the value of Ω M to Ω M = 0.1 and Ω M = 1 to test the dependence of our results on the cosmological assumptions, we accordingly use the values of k UV and k X corresponding to these cosmologies.…”

“…To this end, the community strives to reduce as much as possible the uncertainties on cosmological parameters and to find probes at intermediate redshifts which can be considered standard candles (Yonetoku et al 2004). Given the current interest of the community in quasars as reliable cosmological tools Dainotti et al 2022a; Bargiacchi et al 2022;Khadka et al 2023;Lenart et al 2023), we focus on the hunt for a gold sample for quasars, as already done for gamma-ray bursts (GRBs; Dainotti et al 2010Dainotti et al ,2013Dainotti et al ,2015Dainotti et al ,2016Dainotti et al ,2020Dainotti et al ,2021bDainotti et al ,2022bDainotti et al ,2022cDainotti et al ,2022dDainotti et al ,2023b. We propose an approach to the use of quasars as standard candles similar to the one done for SNe Ia 25 yr ago, but quasars are observed at much larger distances (up to z = 7.54).…”