Inverse Cosmography: testing the effectiveness of cosmographic polynomials using machine learning

Understand

Cosmography has been referred to as a solution to the inverse scattering problem, which is reasonable since it allows us to calculate cosmological bounds from data samplers by performing an expansion of the cosmological observables around present time.

• Nevertheless, this approach is not properly an inverse scattering solution since the method only circumvents the problem to fit the equation of state (EoS) parameters (model-dependent) by replacing it with their fit of its cosmographic parameters (with a polynomial series-dependence).
• Therefore, can we construct a new cosmography approach where the cosmodynamical parameters can be fitted and then employ them to analyse the kinematics via its generic cosmographic parameters? By all means, without experimenting the problem of truncation of the series that all cosmography proposals in the literature argue.
• In this work we present a generic EoS depending solely on the form of $f_i(z)$ and its derivative is found, where this function can be any polynomial (mimicking a dark energy-like term) that allow the dynamics of a specific cosmological density.