FLRW models filled with just dark energy are shown to have a finitepast, since causal geodesics cannot be extended beyond a certainproper time. It is shown that curvature measured along causalgeodesics becomes infinity on travelling to the past, though curvature scalars tend to zero. Furthermore the time measured by free-falling observers from coincidence time to Big Rip is shown to be as short as wished by increasing their linear momentum.