The 35th annual conference on Astronomical Data Analysis Software & Systems 2025 in Görlitz, Germany

In this work, we try to find a set of algorithms to constrain the cosmological parameters using the quasar dataset. Quasars can be the potential cosmic probe that can fill up the gap between the farthest observed Type Ia Supernovae and the Cosmic Microwave Background CMB. Quasars are observed to the highest redshift of z ~ 7.1. It can give valuable insight into the tensions of the cosmological parameters. Use of the quasar dataset on the cosmological parameter constraints is done by the use of an empirical non-linear equation of the luminosity of UV and the luminosity of X-ray of quasar. The main challenge of using the quasar data for Cosmological purposes is to refine the quasar dataset, which is very sparse with a higher intrinsic dispersion. We use different statistical techniques to validate this empirical relation, incorporating the intrinsic dispersion of the dataset. We use both the model-dependent, parametric approach and the non-parametric, model-independent approach to extract valuable information from the dataset. We utilize the idea of different origins of both the quasar and the cosmological parameters to constrain the parameter space. We observe that the strong correlation of the quasar parameter is independent of the cosmology. We introduce a methodology to break this strong correlation between the quasar parameter and the way to explore the model parameter space effectively. We create the Hubble diagram of the quasar dataset with the data compilation of Lusso 2020. We test our methodology in the LCDM model and concretize the algorithm for the application in different dark energy models.