Hubble diagram at higher redshifts: Model independent calibration of quasars

TL;DR

This paper introduces a model-independent method to calibrate quasars as standard candles using Gaussian process regression, enabling the reconstruction of the universe's expansion history up to redshift 7.5 and testing consistency with the ΛCDM model.

Contribution

It presents a novel calibration technique for quasars that does not rely on cosmological models, allowing for high-redshift expansion history reconstruction and model consistency testing.

Findings

Quasars calibrated as standard candles align with ΛCDM at lower redshifts.

Expansion history reconstructed up to redshift 7.5.

High matter density parameter Ω_m consistent with other observations.

Abstract

In this paper, we present a model-independent approach to calibrate the largest quasar sample. Calibrating quasar samples is essentially constraining the parameters of the linear relation between the $\log$ of the ultraviolet (UV) and X-ray luminosities. This calibration allows quasars to be used as standardized candles. There is a strong correlation between the parameters characterizing the quasar luminosity relation and the cosmological distances inferred from using quasars as standardized candles. We break this degeneracy by using Gaussian process regression to model-independently reconstruct the expansion history of the Universe from the latest type Ia supernova observations. Using the calibrated quasar dataset, we further reconstruct the expansion history up to redshift of $z\sim 7.5$. Finally, we test the consistency between the calibrated quasar sample and the standard $\rm{\Lambda}CDM$ model based on the posterior probability distribution of the GP hyperparameters. Our results show that the quasar sample is in good agreement with the standard $\rm{\Lambda}CDM$ model in the redshift range of the supernova, despite of mildly significant deviations taking place at higher redshifts. Fitting the standard $\rm{\Lambda}CDM$ model to the calibrated quasar sample, we obtain a high value of the matter density parameter $\Omega_m = 0.382^{+0.045}_{-0.042}$, which is marginally consistent with the constraints from other cosmological observations.