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The averaging problem on the past null cone in inhomogeneous dust cosmologies

Thomas BuchertHenk van ElstAsta Heinesen
摘要
We investigate average properties of light fronts as they propagate from afinite patch of a source (e.g., the last scattering surface) to a finite patchof a telescope pointing in generic irrotational dust cosmologies. In thissetting we formulate Einstein's field equations on the light fronts and provideconstraint equations and propagation equations along an observer's past nullcone. For the resulting covariant system of area-averaged equations on thelight fronts, we discuss integral-geometric properties together with closureconditions for the underdetermined set of equations. We formulate light frontaverages of observable quantities, including the effective angular diameterdistance and the cosmological redshift drift. The `backreaction' in theeffective angular diameter distance is quantified in terms of cosmologicalarea-averaged variables on the screen space of observation, as well as a`memory function' containing information on the auto-correlation of theexpansion rate of an incoming geodesic null ray bundle along the observer'spast null cone.
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