Institute for Advanced Study/Princeton University Early Universe/Cosmology Lunch Discussion

Light from galaxies across the Universe does not travel on straight lines, as it would in a perfect FLRW universe. This difference between perturbed and unperturbed photon geodesics is due to projection effects – relativistic corrections to the geodesic equation of the photons, along the cosmological observer’s past light-cone. The magnitude of these effects necessitates accounting for them in any measurement of large-scale structure, especially on large scales.

In this talk I will describe a fully relativistic, non-linear, covariant calculation of the galaxy over-density field, as well as the implications of a single observer’s viewpoint on measurements of galaxy clustering statistics, and in particular, on the monopole. I will present a decomposition of the observed galaxy over-density into gauge-invariant observables, each of which has a clear physical meaning. From there, I will move on to show that only differences of potential can be extracted from galaxy clustering data, in agreement with the equivalence principle. The decomposition is independent of the observer’s choice of background – be it the true, global FLRW background, or an inferred one, using the local inferred expansion rate.