[lazulicurio]

My personal (lay) theory is that the global curvature of the universe is flat, but that there are local distortions due to the energy of the big bang/rip.

Two (probably completely inaccurate) thought experiments:

Imagine a sheet of aluminum foil. Crumple it up really tightly into a ball then stretch it back out again. The sheet won't be perfectly flat anymore: it will have ridges and valleys introduced when compressing the sheet. Place objects with mass onto the sheet and those will cause further distortions, but there will be areas without mass that are also distorted.

Imagine a sheet of fabric. Place an object with mass on the sheet, then pull on the sheet (like trying to remove a tablecloth without displacing the tableware). Depending on the velocity of the pull, the mass of the object, and a bunch of other factors, you might introduce ripples into the sheet around the object. Again, distortions in areas without mass. (From my very lay understanding, this would be related to, but independent from, gravitational waves, which are caused by motion of mass in space-time rather than the expansion of space-time itself. But then again, motion is all dependent on the frame of reference, so what do I know?)