Posted: Mar 27, 2017 4:44 pm
Manticore wrote:I keep hearing that the universe is flat, but I would have thought that the increasing rate of expansion implies negative curvature.
No, the curvature is determined by the total density of the universe, and whether it is larger than, equal to, or lower than a particular value at any given time, called the critical density: if the total density is equal to the critical density, then the curvature is zero. If the total density is larger than the critical density, the curvature is positive. If the total density is smaller than the critical density, the curvature is negative. Also, the sign of the curvature cannot change, so if it is zero today, then it has always been zero and it will always remain zero; likewise for positive and negative curvature.
The total density consists of radiation, matter, and dark energy. So in itself, dark energy doesn't determine the sign of the curvature. However, dark energy does have an interesting property: it makes the universe 'flatter'. That is, it pushes the curvature asymptotically closer to zero (if it isn't zero already). Inflation theory relies on the same property, which is one of the reasons why inflation is being proposed to explain why the present-day curvature of our universe is so close to zero.