The ultimate fate of the universe is still unknown because it depends critically on the curvature index k and the cosmological constant Λ. If the universe were sufficiently dense, k would equal +1, meaning that its average curvature throughout is positive and the universe will eventually recollapse in a Big Crunch, possibly starting a new universe in a Big Bounce. Conversely, if the universe were insufficiently dense, k would equal 0 or −1 and the universe would expand forever, cooling off and eventually reaching the Big Freeze and the heat death of the universe. Modern data suggests that the expansion of the universe is accelerating ; if this acceleration is sufficiently rapid, the universe may eventually reach a Big Rip. Observationally, the universe appears to be flat (k = 0), with an overall density that is very close to the critical value between recollapse and eternal expansion.