Gamma-Ray Bursts, Quasars, Baryonic Acoustic Oscillations, and Supernovae Ia: new statistical insights and cosmological constraints

The recent $\sim 4 \, \sigma$ Hubble constant, $H_{0}$, tension is observed between the value of $H_{0}$ from the Cosmic Microwave Background (CMB) and Type Ia Supernovae (SNe Ia). It is a decade since this tension is excruciating the modern astrophysical community. To shed light on this problem is key to consider probes at intermediate redshifts between SNe Ia and CMB and reduce the uncertainty on $H_0$. Toward these goals, we fill the redshift gap by employing Gamma-Ray Bursts (GRBs) and Quasars (QSOs), reaching $z=9.4$ and $z=7.6$, respectively, combined with Baryonic Acoustic Oscillations (BAO) and SNe Ia. To this end, we employ the ``Dainotti GRB 3D relation" among the rest-frame end time of the X-ray plateau emission, its corresponding luminosity, and the peak prompt luminosity, and the ``Risaliti-Lusso" QSO relation between ultraviolet and X-ray luminosities. We inquire the commonly adopted Gaussianity assumption on GRBs, QSOs, and BAO. With the joint sample, we fit the flat $\Lambda$ Cold Dark Matter model with both the Gaussian and the newly discovered likelihoods. We also investigate the impact of the calibration assumed for \textit{Pantheon} and \textit{Pantheon +} SNe Ia on this analysis. Remarkably, we show that only GRBs fulfill the Gaussianity assumption. We achieve small uncertainties on the matter density parameter $\Omega_M$ and $H_0$. We find $H_0$ values compatible within 2 $\sigma$ with the one from the Tip of the Red Giant Branch. Finally, we show that the cosmological results are heavily biased against the arbitrary calibration choice for SNe Ia.