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