Well, several possible ends, actually, all extrapolations form currently known physics. On the other hand, if the universe is closed, it will ultimately stop expanding, and contract back to nothing, ending in a Big Crunch. Overall, Davies paints an optimistic picture of the potentially infinite future, partly in an attempt to counterbalance past authors, from Bertrand Russell to Steven Weinberg, who have been daunted by a vision of a cold, empty, ultimately pointless universe. Davies sees the possibility of a cooling universe, but still full of life and increasing complexity. But I think this shows a confusion between an achievable finite goal, and an ongoing infinite purpose.
Chemistry emerges from physics, biology from chemistry, and intelligence from biology.
It can be like a class of fractal landscapes with its series of higher and grander peaks, yet with no final summit.