  We apply the thermodynamical model of the cosmological event horizon of the
spatially flat FLRW metrics to the study of the recent accelerated expansion
phase and to the coincidence problem. This model, called "ehT model" hereafter,
led to a dark energy (DE) density $\Lambda $ varying as $r^{-2},$ where $r$ is
the proper radius of the event horizon. Recently, another model motivated by
the holographic principle gave an independent justification of the same
relation between $\Lambda $ and $r$. We probe the theoretical results of the
ehT model with respect to the SnIa observations and we compare it to the model
deduced from the holographic principle, which we call "LHG model" in the
following.Our results are in excellent agreement with the observations for
$H\_{0}=64kms^{-1}Mpc^{-1}$, and $\Omega \_{\Lambda
}^{0}=0.63\_{-0.01}^{+0.1}$, which leads to $q\_{0}=-0.445$ and $z\_{T}\simeq
0.965$.
