## What is dust? – Physical foundations of the averaging problem in cosmology

David L. Wiltshire

“The problems of coarse-graining and averaging of inhomogeneous cosmologies, and their backreaction on average cosmic evolution, are reviewed from a physical viewpoint. A particular focus is placed on comparing different notions of average spatial homogeneity, and on the interpretation of observational results. Among the physical questions we consider are: the nature of an average Copernican principle, the role of Mach’s principle, the issue of quasilocal gravitational energy and the different roles of spacetime, spatial and null cone averages. The observational interpretation of the timescape scenario is compared to other approaches to cosmological averaging, and outstanding questions are discussed……………………………..

………………….In summary, it is my view that the apparently accelerated expansion of the universe demands that we take a fresh look at the foundations of cosmological general relativity from ﬁrst principles. In particular, we face the very real possibility that “dark energy” is simply an illusion due to our misunderstanding of gravitational energy gradients in a complex hierarchical geometry. To attack a problem as fundamental as gravitational energy we must think fundamentally.

The argument about whether it is better to use spacetime averages (section 2.3.2) as opposed to spatial averages (section 2.3.3) cannot really be addressed without asking the more basic question of what is the structure of spacetime on the largest of scales, especially over scales larger than that of the matter horizon [19] beyond which the exchange of particles and energy between observers is minimal. Rather than simply taking a principle such as general covariance as being paramount, we have to ask why was general covariance introduced? The reason was that it is a way of characterizing physical laws which combine gravity with the nongravitational interactions of nature in such a way that spacetime geometry is a relational structure between the elementary particles which interact via nongravitational forces.

In seeking to coarse grain gravitational degrees of freedom themselves, we have to be prepared for the possibility that realising spacetime as a relational structure might involve new ingredients beyond those which apply to nongravitational microphysics or general relativity on the scale of isolated systems. For example, the Bianchi I universe picks out preferred directions in space, and is at odds with observation; but would not be admitted by the CEP. Whether the CEP or some other principle is the correct one, what is most important is that we take up the challenges oﬀered by cosmological observations to think more deeply about the foundations of general relativity as a physical theory of the universe…..”

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