We consider the possibility of observing the onset of the late time inflationof our patch of the Universe. The Hubble size criterion and the event horizoncriterion are applied to several dark energy models to discuss the problem offuture inflation of the Universe. We find that the acceleration has not lastedlong enough to confirm the onset of inflation by present observations for thedark energy model with constant equation of state, the holographic dark energymodel and the generalized Chaplygin gas (GCG) model. For the flat $\Lambda$CDMmodel with $\Omega_{m0}=0.3$, 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 theonset 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 theflat holographic dark energy model with $d=1$, we find that $a_v=3.46 a_T$ withthe Hubble horizon and $a_v=2.34 a_T$ with the event horizon, respectively. Forthe flat GCG model with the best supernova fitting parameter $\alpha=1.2$, wefind that $a_v=5.50 a_T$ with the Hubble horizon and $a_v=2.08 a_T$ with theevent horizon, respectively.
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