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

Abstract

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. We test our generic EoS with standard cosmological models and with polynomials proposals as Padé and Chebyshev approximants. Interesting enough, a Padé (2,2) approximant has been considered inside a $f(z)$CDM-like model showing a transition in $z=1$. Also, we found that this is not assured since models with these characteristics have degeneracy and truncation problems that experiment a divergence at this redshift limit. To explore our results, also we present a new supernovae sample trained via a deep learning tool called Recurrent-Bayesian (RNN+BNN) network that can solve problems as overfitting at lower redshifts and increase the density of data points in this region, which can help to discern between cosmographies at 2-$\sigma$ of precision.

31 pages, 17 figures, 20 tables. Accepted by JCAP

References in corpus (6)

• GW190412: Observation of a Binary-Black-Hole Coalescence with Asymmetric Masses
• Extended Gravity Cosmography
• A parametric model for dark energy
• The Dynamics of Quintessence, The Quintessence of Dynamics
• Connecting early and late epochs by f(z)CDM cosmography
• Constraining extra dimensions on cosmological scales with LISA future gravitational wave siren data

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• High-redshift cosmography: Application and comparison with different methods
• Dynamical dark energy models in the light of Gravitational-Wave Transient Catalogues
• Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies
• Tensions with the flat $\mathbf{\Lambda }$CDM model from high-redshift cosmography
• Can high-redshift Hubble diagrams rule out the standard model of cosmology in the context of cosmographic method?
• Neural networks and standard cosmography with newly calibrated high redshift GRB observations
• f(T) cosmology against the cosmographic method: A new study using mock and observational data
• Constraints on Cosmographic Functions of Cosmic Chronometers Data Using Gaussian Processes