Testing the consistency between cosmological data: the impact of spatial curvature and the dark energy EoS

The results of joint analyses of available cosmological data have motivated an important debate about a possible detection of a non-zero spatial curvature. If confirmed, such a result would imply a change in our present understanding of cosmic evolution with important theoretical and observational consequences. In this paper we discuss the legitimacy of carrying out joint analyses with the currently available data sets and explore their implications for a non-flat universe and extensions of the standard cosmological model. We use a robust tension estimator to perform a quantitative analysis of the physical consistency between the latest data of Cosmic Microwave Background, type Ia supernovae, Baryonic Acoustic Oscillations and Cosmic Chronometers. We consider the flat and non-flat cases of the $\Lambda$CDM cosmology and of two dark energy models with a constant and varying dark energy EoS parameter. The present study allows us to better understand if possible inconsistencies between these data sets are significant enough to make the results of their joint analyses misleading, as well as the actual dependence of such results with the spatial curvature and dark energy parameterizations.