I know this may make no sense at all, but how …

I know this may make no sense at all, but how would look like the boundary between our "bubble universe" (where our little observable universe is embebbed) and the rest of the inflationary universe which surrounds it?

One should be full of particles, matter, radiation; the other should be empty space. If you lived close to the edge, you would see a cutoff in galaxies, no CMB, and just a void of an abyss off in the distance.