ABSTRACT
This chapter begins with starts applying general relativity to cosmology, deriving the metric of a homogeneous and isotropic universe. It presents a simple geometric derivation, starting from an insightful two-dimensional analogy. A useful analogy is to consider first a usual two-dimensional surface embedded in an ordinary three-dimensional space. Imposing that the cosmological principle applies to all points of the universe, we obtained three very well-defined spaces: the spherical space, the flat space and the hyperbolic plane. There are, however, speculative cosmological models, within theories with extra spatial dimensions, where in principle we could get information on regions beyond our observable universe. Therefore, it seems that our observable universe is only a small portion of the whole universe and that it makes sense to apply the cosmological principle only to this portion. The two-dimensional analogy will provide a useful pictorial tool for an intuitive understanding of geometrical properties of three-dimensional spaces.
