Connecting early and late epochs by f(z)CDM cosmography

The cosmographic approach is gaining considerable interest as a model-independent technique able to describe the late expansion of the universe. Indeed, given only the observational assumption of the cosmological principle, it allows to study the today observed accelerated evolution of the Hubble flow without assuming specific cosmological models. In general, cosmography is used to reconstruct the Hubble parameter as a function of the redshift, assuming an arbitrary fiducial value for the current matter density, $\Omega_m$, and analysing low redshift cosmological data. Here we propose a different strategy, linking together the parametric cosmographic behavior of the late universe expansion with the small scale universe. In this way, we do not need to assume any "a priori" values for the cosmological parameters, since these are constrained at early epochs using both the Cosmic Microwave Background Radiation (CMBR) and Baryonic Acoustic Oscillation (BAO) data. In order to test this strategy, we describe the late expansion of the universe using the Pad\'e polynomials. This approach is discussed in the light of the recent $H(z)$ values indicators, combined with Supernovae Pantheon sample, galaxy clustering and early universe data, as CMBR and BAO. We found an interesting dependence of the current matter density value with cosmographic parameters, proving the inaccuracy of setting the value of $\Omega_m$ in cosmographic analyses, and a non-negligible effect of the cosmographic parameters on the CMBR temperature anisotropy power spectrum. Finally, we found that the cosmographic series, truncated at third order, shows a better $\chi^2$ best fit value then the vanilla $\Lambda$CDM model. This can be interpreted as the requirement that higher order corrections have to be considered to correctly describe low redshift data and remove the degeneration of the models.