Quasar cosmology: dark energy evolution and spatial curvature

We analyse some open debates in cosmology in light of the most updated quasar (QSO) sample, covering a wide redshift range up to $z\sim7.5$, combined with type Ia supernovae (SNe) and baryon acoustic oscillations (BAO). Indeed, extending the cosmological analyses with high-redshift data is key to distinguishing between different cosmological models that are degenerate at low redshifts, and allowing better constraints on a possible dark energy (DE) evolution. Also, we discuss combinations of BAO, SNe, and QSO data to understand their compatibility and implications for 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 equation of state parameter ($w$), and four flat DE models with variable $w$, namely the Chevallier-Polarski-Linder and Jassal-Bagla-Padmanabhan models, and an "exponential" and Barboza-Alcaniz 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 $\Omega_{M,0}=0.3$ in all data sets assuming a flat $\Lambda \mathrm{CDM}$ model. Yet, all the other models show a statistically significant deviation at 2-3$\sigma$ with the combined SNe+QSO+BAO data set. In the models where DE density evolves with time, SNe+QSO+BAO data always prefer $\Omega_{M,0}>0.3$, $w_{0}<-1$ and $w_{a}>0$. This DE phantom behaviour is mainly driven by SNe+QSO, while BAO are closer to the flat $\Lambda \mathrm{CDM}$ model.