Model Independent Constraints of the Late Time Universe

Present and upcoming surveys of the late time Universe allow increasingly precise cosmological measurements. This makes it possible to characterize further our theory of gravity and fundamental cosmological assumptions. I will first discuss how large-scale effects relevant for upcoming galaxy surveys contribute to constraining our theory of gravity in the context of statistically homogeneous and isotropic models. I will then examine purely geometrical functions based on distance modulus and expansion rate observations, and their implications for the validity of a statistically homogeneous metric.