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.

Conservation laws and the energy–momentum–stress pseudotensor; the cosmological principle and the structure of the universe at large, the Robertson–Walker metric and the Friedman universe(s), Hubble’s law, the expansion of the universe, and the cosmological constant.

With the development of general relativity, Einstein realised that he had a theory which for the first time could be used to create fully self-consistent cosmological models. In 1917, he introduced the cosmological constant to create a static closed Universe.The standard world models were discovered by Friedman in 1922 and 1924 and rediscovered by Lemaitre a few years later. The expansion of the Universe was discovered by Hubble in 1929. A key discovery was that of the cosmic microwave background radiation by Penzias and Wilson in 1965. The resulting hot big bang scenario for the large-scale structure and evolution of the Universe became the preferred cosmological model. With the development of precision cosmology through precise measurements of the cosmic microwave background radiation, it was established that the cosmological constant has a finite value and that the Universe is geometrically flat.