Observational cosmology using characteristic numerical relativity

Abstract

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 Lema\^{\i}tre-Tolman-Bondi (LTB) universe compares to that of the $\ensuremath{\Lambda}$ cold dark matter ($\ensuremath{\Lambda}\mathrm{CDM}$) model given identical observational data on a local observer's past null cone. It is demonstrated that even though observations at the current epoch can be interpreted as either LTB or $\ensuremath{\Lambda}\mathrm{CDM}$, these models have distinctly different histories, and at an earlier epoch, the LTB model will not represent a $\ensuremath{\Lambda}\mathrm{CDM}$ model.