1.1. The global description of the Universe
Ordinarily, the Universe is taken to be a perturbed Robertson-Walker space-time with dynamics governed by Einstein's equations. This is described in detail by Olive and Peacock in this volume. Using the density parameters i for the various matter species and for the cosmological constant, the Friedmann equation can be written
where the sum is over all the different species of matter in the Universe. This equation applies at any epoch, but later in this article we will use the symbols i and to refer to the present values. A typical collection would be baryons, photons, neutrinos, and dark matter (given charge neutrality, the electron density is guaranteed to be too small to be worth considering separately).
The complete present state of the homogeneous Universe can be described by giving the present values of all the density parameters and the present Hubble parameter H0 = 100h km s-1 Mpc-1, and indeed one of the density parameters can be eliminated using eq. (1.1). These also allow us to track the history of the Universe back in time, at least until an epoch where interactions allow interchanges between the densities of the different species, which is believed to have last happened at neutrino decoupling shortly before nucleosynthesis. To probe further back into the Universe's history requires assumptions about particle interactions, and perhaps about the nature of physical laws themselves.