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 } = 64 kms ^ { -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 .

Keywords : dark energy theory , supernova type Ia