Weighed scalar averaging in LTB dust models, part II: a formalism of exact perturbations

Understand

We examine the exact perturbations that arise from the q-average formalism that was applied in the preceding article (part I) to Lemaitre-Tolman-Bondi (LTB) models.

• By introducing an initial value parametrization, we show that all LTB scalars that take a FLRW "look alike" form (frequently used in the literature dealing with LTB models) follow as q-averages of covariant scalars that are common to FLRW models.
• These q--scalars determine for every averaging domain a unique FLRW background state through Darmois matching conditions at the domain boundary, though the definition of this background does not require an actual matching with a FLRW region (Swiss cheese type models).
• Local perturbations describe the deviation from the FLRW background state through the local gradients of covariant scalars at the boundary of every comoving domain, while non-local perturbations do so in terms of the intuitive notion of a "contrast" of local scalars with respect to FLRW reference values that emerge from q-averages assigned to the whole domain or the whole time slice in the asymptotic limit.