Cosmology

Abstract

From the four types of interactions present in our world, only electromagnetism and gravity are long-range interactions. The weak and the strong interactions are so short-ranged that they cannot be responsible for the large-scale behaviour of our universe. However, despite its long range character, electromagnetism cannot be the dominant force in an electrically neutral universe. The only long range interaction that remains is gravity, whose source is energy density. Thus, a theory of the cosmos must be based on a theory of gravity. The best gravitational theory we have so far is Einstein’s theory of General Relativity [9, 10]. In contrast to the Standard Model, which is a quantum field theory, General Relativity is a classical field theory. Aside from this, the distinctive feature of gravity compared to the other fundamental interactions is that it is not a theory defined on space-time, but a theory of space-time itself. The physical foundation of General Relativity is the equivalence principle, which states that gravity uniformly couples to all kind of energy density. Mathematically, space-time is described by a pseudo-Riemannian manifold $\mathcal{M}$ and the gravitational field by the metric field $g_{\mu \nu }(x)$ on $\mathcal{M}$. The gravitational interaction manifests itself geometrically as curvature of space-time.