The fundamental problem considered in this chapter is, how do we relate the FLRW model to the non-uniform real world? The point we emphasize here is that there is a hidden averaging scale in all our descriptions of the universe. There is a hierarchy of different scales of description we can use, with effective equations occurring at each scale. The relation between the descriptions, dynamics, and observations at each of the scales is a key issue. The FLRW model only applies at the largest scales; how does it relate to the inhomogeneities at smaller scales?

A fundamental feature is the non-commutativity of averaging in relation to both dynamics and observations. Through this effect, inhomogeneities in the universe, such as vast walls, filaments, clusters and voids in the distribution of galaxies, can affect both the dynamics and observational properties of the universe. Hence they have the potential to explain at least part, if not all, of the apparent acceleration of the universe indicated by the SNIa data. Note that these are smaller-scale inhomogeneities compared with those considered in the previous chapter, which are of the order of the Hubble scale.

Overall, the question is how to describe the real universe by an (almost) FLRW model, when it is nothing like that on small cosmological scales. What is the meaning of the FLRW metric in relation to the real lumpy universe?

Different scale descriptions

Any mathematical description of a physical system depends on an implicit averaging scale characterizing the nature of the envisaged model (Section 1.4.1), and its tests also have specific scales.