Abstract

In the characteristic formalism of numerical relativity, coordinates are based on null cones generated by radial null geodesics. This formalism is appropriate to cosmology, since nearly all data comes from observations on our past null cone. It is in principle possible to measure the initial data required in order to calculate an evolution into the interior of the past null cone, and codes have been implemented to perform the evolution. In the case of spherical symmetry, it is now possible to apply this process using actual observations leading to constraints on the geometry of the Universe.

On linearization, the formalism may be used to investigate cosmological effects, such as the accelerated expansion, on the propagation of gravitational waves. It is found that the effect of using a de Sitter rather than a Minkowski background for gravitational waves in the LIGO frequency band, is negligible. However, a somewhat counter-intuitive result is found for the gravitational wave energy: energy conservation does not normally apply to inertial observers, but can be formulated for a class of accelerated observers, i.e. with worldlines that are timelike but not geodesic.