Quasar cosmology: dark energy evolution and spatial curvature.

We analyse some open debates in cosmology in the light of the most updated quasar (QSO) sample, covering a redshift range up to $z\sim7.5$, combined with type Ia supernovae (SNe) and baryon acoustic oscillations (BAO) data. Indeed, extending the cosmological analyses with high-redshift data is the key to distinguishing between different cosmological models and allowing a better constraint on dark energy (DE) evolution. Also, we discuss different combinations of the BAO, SNe, and QSO data to understand their compatibility and their implications for the non-flat Universe and extensions of the standard cosmological model. Specifically, we consider a flat and non-flat $\Lambda \mathrm{CDM}$ cosmology, a flat and non-flat DE model with a constant DE EoS parameter ($w$), and four flat DE models with variable $w$: Chevallier-Polarski-Linder, Jassal-Bagla-Padmanabhan, an "exponential" and "rational" parameterisations. We find that a joint analysis of QSO+SNe with BAO is only possible in the context of a flat Universe. Indeed BAO confirms the flatness condition assuming a curved geometry, whilst SNe+QSO show evidence of a closed space. We also find that the matter component is fully consistent with $\Omega_{M,0}=0.3$ in all the data sets assuming a flat $\Lambda \mathrm{CDM}$ model. Yet, all the other analysed models show a statistically significant deviation at $>3\sigma$ from this prediction by making use of the SNe+QSO sample, which remains still significant (2-3$\sigma$) with the combined SNe+QSO+BAO data set. In the models where the DE density evolves with time, the SNe+QSO+BAO data always prefer $\Omega_{M,0}>0.3$, $w_{0}<-1$ and $w_{a}$ greater, but statistically consistent, than $w_{a}=0$. This DE phantom behaviour is mainly driven by the contribution of SNe+QSO, while BAO are closer to the prediction of the flat $\Lambda \mathrm{CDM}$ model (also due to their large uncertainties).