Hubble diagram at higher redshifts: model independent calibration of quasars

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 data set, we further reconstruct the expansion history up to redshift of z similar to 7.5. Finally, we test the consistency between the calibrated quasar sample and the standard Lambda cold dark matter (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 Lambda CDM model in the redshift range of the supernova, despite the 2-3 sigma significant deviations taking place at higher redshifts. Fitting the standard Lambda CDM model to the calibrated quasar sample, we obtain a high value of the matter density parameter Omega(m) = 0.382(-0.042)(+0.045), which is marginally consistent with the constraints from other cosmological observations.

Automated summary

This study presents a model-independent approach to calibrate the largest quasar sample and use quasars as standardized candles. The calibrated quasar sample shows good agreement with the standard ΛCDM model in the redshift range of supernovae.