3D flat space on cosmological scales requires no new imagination. It's the same geometry that you are already intimately familiar with.
If you held two laser pointers side by side so they emit parallel beams, then those beams stay parallel forever. That's a feature of flat geometry.
Observations are consistent with the space being flat, but it could also be slightly positively or negatively curved. In fact it would be very easy for it to be either of those. If the density of the universe turns out to be slightly more than the critical density, then space is positively curved. If slightly less than the critical density, then space is negatively curved. Positive curvature would make those two laser beams come together after some distance, just like lines of longitude come together on the Earth. Negative curvature would instead spread them apart.
For space to curve back on itself to make the volume of the universe finite (the entire thing, not just the observable part), and so that going far enough in any direction brings you back to where you started, then the space needs to be positively curved. It's entirely possible that this is how the universe really is, since with the uncertainties in the measurements it's a roughly 50-50 chance the density is greater than the critical density.
By the way, I've thrown the term "critical density" out there a few times, but I don't think I defined what it is yet. It is the specific density of matter and energy that would make the universe flat. Which is just the reverse of what I've already said, so that's not helpful. What's helpful is that it works out to be about 5 to 6 proton masses per cubic meter (the exact number depends on the value of the Hubble constant today), and as a formula it is given by
where H is the Hubble constant and G is the gravitational constant. We can also write it as 0.001123 protons per cubic meter times H2
, if H is in km/s/Mpc.
5 or 6 protons for each cubic meter in space needed to make the universe flat might sound very tiny. It is
tiny, even compared to the density of the interstellar medium, which is a better vacuum than anything we can make on Earth. But it's greater than the density of a typical "void" in the cosmic web. So on the average, the density of the universe works out to be pretty darn close to the critical density, which is a pretty surprising coincidence (not just for making the geometry flat), and as you mentioned, ALEX, the leading idea for why it works out that way has to do with the inflationary hypothesis. Maybe more on that topic, later.