The standard approach to cosmology is a model-based approach: find the simplest possible model of spacetime that can accommodate the observational data. An alternative is a direct observational approach. The first method determines observational relations and parameters from a model; the second attempts to determine a model from observational relations. We introduce the latter method in this chapter, and it will also feature in Chapter 15; the former is essentially used in the rest of this book.

As mentioned before, a fundamental feature of cosmology is that there is only one universe, which we cannot experiment on: we can only observe it, and moreover, on a cosmological scale, only from one specific spacetime event. Observations therefore give direct access only to our past light-cone, at one cosmological time. How can we then devise and test suitable cosmological models?

Model-based approach

In the standard approach, one chooses a family of models first, characterized by as few free parameters and free functions as possible. Then one fixes these parameters and functions in order to reproduce astronomical observations as accurately as possible. Therefore this is in fact a form of light-cone best-fitting procedure: one is obtaining a best-fit of the chosen family of models to the real universe via comparison of observational relations predicted by the model with actual observations.

Traditionally, this is applied almost exclusively to the FLRW models. The merit of the approach is that it has good explanatory power, which serves as a vindication of the chosen models.