Non-parametric reconstructions of cosmic curvature: current constraints and forecasts

The assumption of a flat Universe that follows the cosmological principle, i.e., that the universe is statistically homogeneous and isotropic at large scales, comprises one of the core foundations of the standard cosmological model -- namely, the $\Lambda$CDM paradigm. Nevertheless, it has been rarely tested in the literature. In this work, we assess the validity of this hypothesis by reconstructing the cosmic curvature with currently available observations, such as Type Ia Supernova and Cosmic Chronometers. We do so by means of null tests, given by consistency relations within the standard model scenario, using a non-parametric method -- which allows us to circumvent prior assumptions on the underlying cosmology. We find no statistically significant departure from the cosmological principle and null curvature in our analysis. In addition, we show that future cosmological observations, specifically those expected from Hubble parameter measurements from redshift surveys, along with gravitational wave observations as standard sirens, will be able to significantly reduce the uncertainties of current reconstructions.