Observational cosmology using characteristic numerical relativity: Characteristic formalism on null geodesics

Abstract

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.

Towards the geometry of the Universe from data

“…Instead the ideal is to model late time processes as accurately as possible and constrain the geometry of the universe based on data gathered with these models. Such an approach would be complementary to that employed in Redlich et al (2014) and Zibin & Moss (2014) for example. Both approaches should ultimately arrive at the same conclusions.…”

“…To keep it as concise as possible we have omitted some details. In particular we refer the reader to that paper, and van der Walt & Bishop (2012), for further details regarding our formulation of the observational and CIVP formalism. The paper is structured as follows: the next section highlights some key differences between the ΛLTB and FLRW models that we exploit to test for radial inhomogeneity.…”

Numerically reconstructing the geometry of the Universe from data

“…Together with the value of the cosmological constant Λ, samples of these two functions completely specify a ΛLTB model. The geometry of the Universe can then be solved for numerically by using observational coordinates [1] to pose the Einstein field equations (EFE) as a characteristic initial value problem (CIVP) (see [4] and [5] for details). Once the form of the metric is known it can be used, in conjunction with the forms of the fluid variables ρ and u a , to compute any observable as a function of redshift z.…”

The characteristic formalism: Cosmology constructed from observational data

“…Over the last few years, numerical relativity codes for computing gravitational waves on future null cones have been adapted to cosmology, 3,4 and very recently real data has been used within this approach to investigate whether cosmological models are consistent with observations. 5 This article reviews the mathematical development of this field, and provides the background for a companion article in these Proceedings on results using actual data.…”