According to general relativity, mass and energy cause the curvature of space. To have perfectly flat space, there must be a completely empty vacuum state with no mass or energy.
Theoretically, is it possible to create perfectly flat space, even locally, by precisely arranging mass and energy in the universe?
I am not a physics major nor have I studied physics in depth; I am an ordinary person.
In principle, you would have flat spacetime in the hollow center of a spherically symmetric mass/energy distribution. So you could imagine rearranging the contents of the Universe into such a configuration.
However, most of the energy content of the Universe is dark energy. We are not sure that it even makes sense to talk about moving dark energy from one place to another. If dark energy is uniformly distributed everywhere, as in the simplest models, then it induces spacetime curvature everywhere, which you will never be able to remove or compensate.
No, since you're not going to be able to evacuate the vacuum energy. Thus you cannot get a perfectly flat space theoretically. However, at most humanly probeable scales today, it would appear flat.
