The event horizon thermodynamical (ehT‐) model of the dark energy

We present the main results of a model, namely the event-horizon model, based on a thermodynamical approach for the law of Lambda(t). We consider a phenomenological model where we give to the effective cosmological 'constant' Lambda the physical meaning of a 'vacuum' energy density, as usually admitted. In the same vein as the generalization of the black holes [1][2] and of the de Sitter event-horizon thermodynamics [3][4] to the FLRW space-time, we associated to this 'vacuum' energy density a full thermodynamics for cosmological event horizons without further microscopic precision about the fields describing the vacuum. Without any ansatz and using thermodynamics arguments, we then deduce the law Lambda proportional to r(-2) where r is the proper radius of the event horizon in quasi-de Sitter FLRW spatially flat spacetime. With this relation, the coincidence problem is solved by the decay of Lambda(t) due to the expansion of the universe. We apply this model to the study of the recent accelerated expansion phase and to the coincidence problem. Finally, we introduce a logarithmic corrective term in the entropy associated to the DE, which leads to a new term in the DE density. This term was derived for any thermodynamical system encountering fluctuations around an equilibrium state [16]. This corrective term was first applied to black hole. Because of the analogy between the cosmological FLRW event horizon and the Black hole event horizon, it seems legitimate to introduce this corrective term in the entropy of Lambda. After a numerical resolution, we compute the evolutions of the main cosmological parameters: Lambda(t), the Hubble parameter H(t), the vacuum density Omega(Lambda)(t). The computed values are compatible with an initial inflation, and the current observations of the 'concordance' model. It also predicts a graceful exit of early inflation and the present acceleration and solves in the same time the age and the coincidence problem.