Classifying the Future of Universes with Dark Energy

We classify the future of the universe for general cosmological models including matter and dark energy. If the equation of state of dark energy is less then -1, the age of the universe becomes finite. We compute the rest of the age of the universe for such universe models. The behaviour of the future growth of matter density perturbation is also studied. We find that the collapse of spherical overdensity region is greatly changed if the equation of state of dark energy is less than -1.