The expansion continues, and gravity works to pull it back. Take matter alone first and follow that contest. What settles it is how much the universe holds.
There is a density that would bring the expansion exactly to a halt. It is called the critical density, and the actual density divided by it is written .
If , gravity wins. The expansion halts at some point and turns into a contraction. If , it never halts and goes on widening forever.
Exactly is the dividing line. The expansion never stops, but it slows without limit. The curves are indistinguishable at first; they part only much later.
So what is the actual ? Count up what the universe contains and it follows.
Stars, gas, the atoms our bodies are built from: all this ordinary matter comes to about % of the whole. The abundances of the light elements are what told us the amount.
The dark matter that the rotation curves demanded is %. It gives off no light, so it is unseen, but through gravity it plainly tells. There is more than times as much of it as of ordinary matter.
The remaining % is dark energy. The add to , which is to say exactly the critical density. But dark energy works against gravity, so even at the expansion does not stop.
What the density fixes is not only the ending. It fixes the shape of space as well, because in general relativity space itself curves where there is matter.
In curved space the geometry of the plane fails. The plainest sign of it is the sum of the angles of a triangle.
If the density is above critical, space curves closed, like the surface of a sphere. The sides of a triangle bow outward and the angles sum to more than .
Below critical it bows the other way and the sum falls short of . At exactly critical the sum is : space is flat. Measuring and measuring the curvature of space are one and the same thing.
One cannot draw a triangle across the sky and measure its angles. Instead one puts an object of known size far away and measures the angle it subtends.
If space curves closed, the lines of sight converge and the same object looks larger. If it is open, it looks smaller. The angle subtended reports the curvature directly.
The ruler for this is the blotches of the background radiation. Their size is set by how far sound had travelled by the time of the clearing, and it can be calculated rather than measured.
The angle came out matching the prediction for flat space: . But % of that total is dark energy, so flat or not, the expansion does not stop. It goes on widening, and speeding up as it goes.