The Universe can be geometrically flat, but topologically finite and closed!

[notFritzArgelander]

I made an error in responding in this thread which I hope to correct with this post.

The folks in the OP constructed a straw man argument that the universe "could be topologically finite and closed". The only way this stands up by introducing new cosmological parameters to deal with the curvatures of the toroidal topologies (i.e. doughnuts) they propose. One can then avoid falsification by increasing the radii of curvature arbitrarily. That was my objection, the avoidance of falsifiability.

Now the "straw man" here is that they only consider the consensus model, i.e. the parameters found here:
https://en.wikipedia.org/wiki/Lambda-CD ... Parameters

They do not consider the errors inherent in the parameter set. When one considers the extended parameter set which allows one to look more closely at trends one finds an interesting value for Omega _tot = 0.9993±0.0019.

The significance of this is that a universe can only be topologically finite and closed if Omega _tot > 1.0000.

So the straw man is that Omega _tot = 1.0000 exactly. Anything less than 1.0000 says that the universe is open and infinite with positive total energy. Only Omega _tot =1.0 exactly corresponds to finite infinite and flat. The data error analysis is slightly in favor of an open topology already so already there is only a 1 in 3 chance of a closed topology.

I expect that as more data is accumulated that the errors will shrink. With the data already biased in favor of an open universe this closed universe can still hide behind the errors.

If one is annoyed by phrases such as the use of "is" in "the universe is open and flat" one could choose to continue to suffer from that, or one could simply read for "is" the "X is Y within the error limits of currently available observations". Scientists use "X is Y" as a shorthand for "X is Y within the error limits of currently available observations" which is a much more cumbersome phrase.

So I apologize for missing the point that this idea already has only a 1 in 3 chance.

[turboscrew]

I wonder if there's anything that could be measured with absolute precision and accuracy. In theory, you can calculate that way, but to test the calculations against reality, that'll always happen "within the error limits of currently available observations". And then the "within the error limits of currently available observations" is redundant.

[notFritzArgelander]

I wonder if there's anything that could be measured with absolute precision and accuracy. In theory, you can calculate that way, but to test the calculations against reality, that'll always happen "within the error limits of currently available observations". And then the "within the error limits of currently available observations" is redundant.

Indeed no such thing is possible. The flat infinite universe can only be shown to be false, it can never be shown to be true. There’s an esthetic reason for preferring it as long as it’s within the error bounds: it costs exactly zero energy (density) to make such a universe. The slightly favored open infinite curved version requires an external source of energy.