What's inside the cone? Numerically reconstructing the metric from observations

We investigate the possibility of using Gaussian process regression to smooth data on the current past null-cone for use as the input to a relativistic integration scheme. The algorithm we present is designed to reconstruct the metric of spacetime within the class of spherically symmetric dust universes, with or without a cosmological constant. Assuming that gravity is well described by General Relativity, we demonstrate how the algorithm can be employed to test the Copernican principle based on currently available observations. It is shown that currently available data is not sufficient for a conclusive result. The intrinsic noise present in realistic data presents a challenge for our smoothing algorithm and we discuss some of its limitations as well as possible extensions to it. We conclude by demonstrating how a direct determination of the cosmological constant is possible using redshift drift data.