Modelling and testing the equation of state for (Early) dark energy
  A general equation of state is considered for analysing the possible
behaviors for (Early) dark energy that alleviates the Hubble parameter tension
problem. By departing from the possible evolution for the (Early) dark energy
density and the corresponding dynamical equations, the equation of state is
obtained, which allow us to analyze qualitatively the cosmological evolution
and the dominance of each term in the equation of state along the cosmic
expansion, which show some interesting consequences as the occurrence of (past)
future singularities. Then, by considering two general models, their free
parameters are fit with different sources of data, showing the goodness of the
fits in comparison to more standard models. Results might be considered as a
promising starting point to get a better understanding of the cosmological
evolution as a whole.
