Gravity seminar: Pierre Mourier, Universitat de les Illes Balears

Title: The averaging problem in relativistic cosmology: the consequences of spatial inhomogeneity and the choice of space+time split

Abstract: The standard model in cosmology relies on a spatially homogeneous and isotropic background spacetime, idealizing the statistical homogeneity and isotropy observed in matter distribution at very large scales. The formation of matter structures (galaxy clusters, filaments, voids…) may then be described as linear perturbations or Newtonian dynamics on top of this expanding background. The simplicity of the background model comes at a cost: to match observations, its expansion must be accelerating in recent times, which in turns requires either an exotic Dark Energy fluid, or a cosmological constant whose order of magnitude is challenging to explain. It has also led to some further observational “tensions” in recent years, most famously discrepancies in the measurement of the current expansion rate H0.

On a more fundamental level, there is no clear a priori prescription of how such a homogeneous background can be extracted from the actual inhomogeneous Universe: this is the “averaging problem”. I will first present a simple spatial averaging framework to smooth out local inhomogeneities in scalar observables (matter density, curvature, expansion rate…) in GR, and the resulting effective large-scale dynamics. Those include additional “backreaction” terms from the presence of structure that can, in principle, contribute to the effects of dark energy and/or dark matter at different scales. A specific issue of building such a scheme in a relativistic spacetime is the many ways one can choose to define “space” as 3-dimensional slices to characterize spatial observables evolving with time. This has led in particular to concerns about the dependence of the effective dynamics in such a choice. I will show how to define an averaging framework which can be applied to any spatial slicing, especially useful e.g. for the interpretation of relativistic cosmological simulations. Using this, I will then discuss more directly the dependence of spatial averages on the slicing, following arXiv:2401.09170. I will show in particular how physical restrictions can be applied on possible slicings to ensure an approximate invariance of averages.