Ideal observational cosmology

Following Kristian and Sach's direct observational approach to cosmology, this paper analyses in detail the information that can be obtained from idealised astronomical observations, firstly in the cosmographic case when no gravitational field equations are assumed, and secondly in the cosmological case when Einstein's field equations of General Relativity are taken to determine the space-time structure. It is shown that if ideal observations are available, in the cosmographic case they are insufficient to determine the space-time structure on the past light cone of the observer; however in the cosmological case they are precisely necessary and sufficient to determine the space-time geometry on the light cone and in its causal past (at least down to where caustics or curps first occur). The restricted case of spherically symmetric space-times is analysed in detail, and necessary and sufficient observational conditions that such a space-time be spatially homogeneous are proven. A subsequent paper will examine the situation of realistic observational data.