Theory of Observations in the Relativistic Zone

Abstract

General Relativity, with the hypothesis of a universe filled with a perfect fluid of density p and pressure p and a space that is isotropic with respect to the Earth, furnishes us with a cosmological solution whereby spacetime acts like a space with a radius of curvature R(t) the same everywhere but varying in the course of cosmic time t; the ds² of Robertson-Walker, p and p are given as a function of R(t), R(t) depending finally on the equation of state p = p(ρ) for a perfect fluid. In this chapter we give the basics governing the theory of observations made in the rela-tivistic zone, for an arbitrary function R(t). We apply the results particularly to the most interesting examples of the Friedmann universes — corresponding to p = 0 (and ⋀ = 0) — and, especially, to the Einstein-de Sitter model — corresponding in addition to the Euclidean case. Of course, this theory gives the usual classical non-relativistic Euclidean solutions for observations in the local neighbourhood.