## Cosmological Non-Linearities as an Effective Fluid

We know our Universe is inhomogeneous, comprising regions of high density (galaxies and clusters of galaxies) as well as regions of much lower density (e.g. cosmic voids). Our standard cosmological models are based on exact solutions of Einstein’s equations of general relativity that assume homogeneity and isotropy. The general assumption is that if we confine ourselves to large enough scales the effect of the clumpiness of matter can either be disregarded or treated using perturbation theory. As far as we can tell, that approach works reasonably well but we know it must fail on smaller scales where the structure is in the non-linear regiome where it can’t be described accurately using perturbation theory because the fluctuations are so large.

From time to time I’ve idly wondered whether it might be possible to understand the effect of these non-linearities in general relativity by treating them as a kind of fluid with an energy-momentum tensor that acts as a correction to that of the perfect fluid form of the background cosmological model. This would have to be done via some sort of averaging so it would be an effective, coarse-grained description rather than an exact treatment. It is clear though that non-linearities would generate departures from the perfect fluid form, particularly resulting in off-diagonal terms in the energy-momentum tensor corresponding to anisotropic stresses (e.g. viscosity terms).

Anyway, a recent exchange on Twitter relating to a new paper that has just appeared revealed that far cleverer people than me had looked at this in quite a lot of detail a decade ago:

You can find the full paper here.

There are quite a lot of subtleties in this – how to do the spatial averaging, how to do the time-slicing, etc – which I don’t fully understand but at least I’m reassured that it isn’t a daft idea to try thinking of things this way!

P.S. The relativistic simulations reported in this paper could in principle be used to estimate the parameters mentioned in the abstract above, if that hasn’t been done before!

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November 28, 2020 at 11:26 am

People who have worked on the gauge gravity theory known as Einstein-Cartan-Kibble-Sciama have generated corrections to the Friedmann equations of this sort. Anthony Lasenby is not the first but he probably does it the most clearly.