The characteristic formalism in numerical relativity, which has been developed to study gravitational waves, and the observer metric approach in observational cosmology both make use of coordinate systems based on null cones. In this paper, these coordinate systems are compared and it is then demonstrated how characteristic numerical relativity can be used to investigate problems in observational cosmology. In a numerical experiment using the characteristic formalism, it is shown how the historical evolution of a LTB universe compares to that of the ΛCDM model given identical observational data on a local observer's past null cone. It is demonstrated that, at an earlier epoch of the LTB model, the observational data would not be consistent with that of the ΛCDM model.

The characteristic formalism of numerical relativity is based on a system of coordinates aligned with outgoing null cones. While these coordinates were designed for studying gravitational waves, they can also be easily adapted to model cosmological past null cones (PNCs). Similar to observational coordinates in the observational approach to cosmology, this then provides a model that only makes use of information causally connected to an observer. However, the diameter distance, which is used as a radial coordinate, limits the model's cosmological application to the region prior to the PNC refocusing. This is because after refocusing, the diameter distance ceases to be a unique measure of distance. This paper addresses the problem by introducing a metric based on the Bondi-Sachs metric where the radial coordinate is replaced by an affine parameter. A model is derived from this metric and it is then shown how an existing numerical scheme can be adapted for simulation of cosmological PNC behavior. Numerical calculations on this model are found to have the same stability and convergence properties as the standard characteristic formalism.

Abstract. 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.

In this paper we show that there are circumstances in which the damping of gravitational waves (GWs) propagating through a viscous fluid can be highly significant; in particular, this applies to Core Collapse Supernovae (CCSNe). In previous work, we used linearized perturbations on a fixed background within the Bondi-Sachs formalism, to determine the effect of a dust shell on GW propagation. Here, we start with the (previously found) velocity field of the matter, and use it to determine the shear tensor of the fluid flow. Then, for a viscous fluid, the energy dissipated is calculated, leading to an equation for GW damping. It is found that the damping effect agrees with previous results when the wavlength λ is much smaller than the radius r i of the matter shell; but if λ r i , then the damping effect is greatly increased.Next, the paper discusses an astrophysical application, CCSNe. There are several different physical processes that generate GWs, and many models have been presented in the literature. The damping effect thus needs to be evaluated with each of the parameters λ, r i and the coefficient of shear viscosity η, having a range of values. It is found that in most cases there will be significant damping, and in some cases that it is almost complete.

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