We consider the possibility of observing the onset of the late time inflation of our patch of the Universe .
The Hubble size criterion and the event horizon criterion are applied to several dark energy models to discuss the problem of future inflation of the Universe .
We find that the acceleration has not lasted long enough to confirm the onset of inflation by present observations for the dark energy model with constant equation of state , the holographic dark energy model and the generalized Chaplygin gas ( GCG ) model .
For the flat \Lambda CDM model with \Omega _ { m 0 } = 0.3 , we find that if we use the Hubble size criterion , we need to wait until the a _ { v } which is the scale factor at the time when the onset of inflation is observed reaches 3.59 times of the scale factor a _ { T } when the Universe started acceleration , and we need to wait until a _ { v } = 2.3 a _ { T } to see the onset of inflation if we use the event horizon criterion .
For the flat holographic dark energy model with d = 1 , we find that a _ { v } = 3.46 a _ { T } with the Hubble horizon and a _ { v } = 2.34 a _ { T } with the event horizon , respectively .
For the flat GCG model with the best supernova fitting parameter \alpha = 1.2 , we find that a _ { v } = 5.50 a _ { T } with the Hubble horizon and a _ { v } = 2.08 a _ { T } with the event horizon , respectively .