No. The input into the equation is the density of matter in space, nothing having to do with the size of the observable universe. On large scales in the visible universe, matter is fairly evenly distributed at a density of about 1 atom of hydrogen per cubic meter.
For any constant nonzero density form of matter, if you pack enough of it together in a sphere in a flat spacetime, its Schwarzchild radius will eventually exceed its radius. This is because the Schwarzchild radius is proportional to the mass, but the radius of the actual matter is proportional to the cube-root of the mass.
It's a fun thought experiment, but not physically meaningful in this universe because our spacetime is expanding, and the original calculations assume there's nothing at the edge pulling 'outward', but in our universe there is.
Thank you, you're adding more concrete verbiage to my suspicions that my calculations were too naive: I was only doing classical, pre-General-Relativity, calculations. On such large scales, the dynamic nature of spacetime itself would play an important role. Especially if, as evidence suggests, gravitational waves travel no faster than light.
> For any constant nonzero density form of matter, if you pack enough of it together in a sphere in a flat spacetime, its Schwarzchild radius will eventually exceed its radius.
You can't do this in flat spacetime, because the matter curves spacetime, and the denser you pack it, the more it curves spacetime.
The point of the thought experiment was that you start with a universe with no other matter in it that's not expanding, both of which conditions our universe violates.
For any constant nonzero density form of matter, if you pack enough of it together in a sphere in a flat spacetime, its Schwarzchild radius will eventually exceed its radius. This is because the Schwarzchild radius is proportional to the mass, but the radius of the actual matter is proportional to the cube-root of the mass.
It's a fun thought experiment, but not physically meaningful in this universe because our spacetime is expanding, and the original calculations assume there's nothing at the edge pulling 'outward', but in our universe there is.