Hi Dimitri, welcome to PF.
This is a question about cosmology, and should be put in the relevant subforum if you want the best answers.
I'll ask mods for the thread to be moved.
Dmitri Martila said:
The (most popular) flat model of Universe is space-infinite. How the infinity is measured? Can you give me references to the papers about the actual infinity of space?
There aren't any, because the spatial extent of the universe as a whole is not part of the model, nor can you ever measure anything from beyond the cosmic event horizon.
As rootone said, the extent of the whole can be inferred from the model, depending on its measurable parameters, and as long as you make some assumptions about homogeneity and topology. Infinity is what you get with the simplest assumptions (cosmological principle holds everywhere, and topology is not exotic) and zero curvature.
This is hardly the same as stating that the universe IS infinite. After all, laws of physics
may be different in other regions of the universe, and even a flat universe can be finite if it's shaped like e.g. a 4D torus.
Dmitri Martila said:
It is the measurement of local curvature. I am talking about the measurement of the diameter of the Universe by the ruler.
As long as by 'local' you mean whole of the observable universe. Curvature measurements use CMBR, so it's the longest ruler you can get. The most recent such measurements can be found in PLANCK mission's 2015 results papers.
