8.2.2. Model Dependent Calibration

The model dependent procedure fixes the background cosmology with a given cosmological model, where typically the dark energy evolution is assumed a priori. Since the background cosmology<sup>24</sup> enters the correlation functions, generically in the form *y* = *ax* + *b*; this means that one has to (1) assume a background cosmology, (2) fix the most suitable numerical bounds over the free coefficients of the background cosmology, and (3) calibrate the correlation.

As it appears evident, this strategy consists of determining an accredited cosmological model with particular choices of the free parameters, determined elsewhere.

This procedure is obviously strongly plagued by the circularity problem. It fixes the cosmological evolution with a given model and does not permit constraining suitably another cosmological paradigm. In fact, if one calibrates with a generic model, say *H*(1) (*z*), any other statistical expectations on a different model, say *H*(2) (*z*), would favor the model that better matches *H*(1) (*z*). In other words, calibrating with *H*(1) (*z*) implies that the best fits are statistically argued for *H*(2) (*z*) ' *H*(1) (*z*).

Another dramatic fact is that one has to constrain the free parameters of the background scenario by means of additional fits, with different data sets. This implies that an overall analysis would be plagued by error propagation between different catalogs of data and limits severely the analysis itself. To avoid other fits, one can assume exact versions of the cosmological models that should be used as backgrounds. In such a way, the corresponding error propagation reduces, albeit one does not take a real tested cosmological scenario, but rather a simplified version of it.
