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 other words , we want to develop a cosmographic approach without assuming any background model but considering a f ( z ) CDM model where the function f ( z ) is given by a suitable combination of polynomials capable of tracking the cosmic luminosity distance , replacing the cosmological constant \Lambda .
In order to test this strategy , we describe the late expansion of the universe using the Padé polynomials .
Specifically , we adopt a P ( 2 , 2 ) series , that is a promising rational series which guarantees a good convergence also at high redshift .
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 .
Furthermore , a non-negligible effect of the cosmographic parameters on the CMBR temperature anisotropy power spectrum is shown , and constraints by selected joint datasets are reported .
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 .