Having developed the necessary mathematics in chapters 4 to 6, chapter 7 returns to physics Evidence for homogeneity and isotropy of the Universe at the largest cosmological scales is presented and Robertson-Walker metrics are introduced. Einstein’s equations are then used to derive the Friedmann equations, relating the cosmic scale factor to the pressure and density of matter in the Universe. The Hubble constant is discussed and an analytic form of the red-shift distance relation is derived, in terms of the matter density, the cosmological constant and the spatial curvature, and observational values of these three parameters are given. Some analytic solutions of the Friedmann equation are presented. The cosmic microwave background dominates the energy density in the early Universe and this leads to a description of the thermal history of the early Universe: the transition from matter dominated to radiation dominated dynamics and nucleosynthesis in the first 3 minutes. Finally the horizon problem and the inflationary Universe are described and the limits of applicability of Einstein's equations, when they might be expected to break down due to quantum effects, are discussed.

The success of the standard cosmological model with a finite cosmological constant raises many problem for fundamental physics. The inflationary model of the very early Universe provides a solution to a number of these problems but it requires the introduction of new physics. There is no physical realisation of the inflaton field. The model has, however, had a notable success in accounting for the origin of the fluctuations from which galaxies and the large-scale structure of the Universe formed. A solution to the origin of the baryon asymmetry of the Universe has yet to be found. Many cosmologists believe that the solution to these problems lies in the very earliest epochs, the Planck era, when gravity itself has to be quantised.