So I know that the rate of expansion of the universe is increasing, i.e. the 2nd time derivative of the size of the universe is positive. But, is the next time derivative (i.e. 3nd time derivative of the size of the universe) positive of negative? Do we have enough information to determine this? And lastly would a negative value indicate that eventually the expansion of the universe at some point in the future start slowing down, lead the rate of expansion to slow down and eventually become negative, and allow the possibility of a contracting universe in the very very very distant future? A theoretical example (of a negative value of my above question) would be if spacetime cannot be infinitely stretched, and acts somewhat like a spring with some optimum amount of being stretched. We would still be in the "over-compressed" stage, and the extensive force causes the spring to accelerate back to it equilibrium position, but that amount of acceleration would be less and less as the spring approached its equilibrium position. Then at some point the spring passes through its equilibrium position , and a tensional force takes over to prevent further expansion. This creates a cycle (with period in the order of billions and billions of years, we would still be in the first half cycle) that could repeat infinitely (if no energy is lost per cycle) or which would decay in amplitude every cycle and eventually settle into the equilibrium position. spacetime would be a logical 3D (or 4D) extension of this scenario. I know these ideas can't be proven, I'm just wondering if they could in theory be possible.