An approach to cold dark matter deviation and the $H_{0}$ tension
  problem by using machine learning
  In this work, two different models, one with cosmological constant $\Lambda$,
and baryonic and dark matter (with $\omega_{dm} \neq 0$), and the other with an
$X$ dark energy (with $\omega_{de} \neq -1$), and baryonic and dark matter
(with $\omega_{dm} \neq 0$), are investigated and compared. Using Bayesian
machine learning analysis, constraints on the free parameters of both models
are obtained for the three redshift ranges: $z\in [0,2]$, $z\in [0,2.5]$, and
$z\in [0,5]$, respectively. For the first two redshift ranges, high-quality
observations of the expansion rate $H(z)$ exist already, and they are used for
validating the fitting results. Additionally, the extended range $z\in [0,5]$
provides predictions of the model parameters, verified when reliable
higher-redshift $H(z)$ data are available. This learning procedure, based on
the expansion rate data generated from the background dynamics of each model,
shows that, at cosmological scales, there is a deviation from the cold dark
matter paradigm, $\omega_{dm} \neq 0$, for all three redshift ranges. The
results show that this approach may qualify as a solution to the $H_{0}$
tension problem. Indeed, it hints at how this issue could be effectively solved
(or at least alleviated) in cosmological models with interacting dark energy.
