Swampland criteria and neutrino generation in a non-cold dark matter universe

In this paper, the implications of string Swampland criteria for a dark energy-dominated universe, where we have a deviation from the cold dark matter model, will be discussed. In particular, we have considered two models. One of them is one parameter model, while the second one has been crafted to reveal the dynamics in the deviation. The analysis has been obtained through the use of Gaussian processes (GPs) and $H(z)$ expansion rate data (a $30$-point sample deduced from a differential age method and a $10$-point sample obtained from the radial BAO method). We learned that the tension with the Swampland criteria still will survive as in the cases of the models where dark matter is cold. In the analysis besides mentioned $40$-point $H(z)$ data, we used the latest values of $H_{0}$ reported by the Planck and Hubble missions to reveal possible solutions for the $H_{0}$ tension problem. Finally, the constraints on the neutrino generation number have been obtained revealing interesting results to be discussed yet. This and various related questions have been left to be discussed in forthcoming papers.