Notice how this solves the horizon problem in that our present Universe was simply a small piece of a larger Big Bang universe that was all in causal connection before the inflation era. Other bubble universes might have very different constants and evolutionary paths, but our Universe is composed of a small, isotropic slice of the bigger Big Bang universe. Inflation also solves the flatness problem because of the exponential growth. Imagine a highly crumbled piece of paper. This paper represents the Big Bang universe before inflation.
Inflation is like zooming in of some very, very small section of the paper.
If we zoom in to a small enough scale, the paper will appear flat. Our Universe must be exactly flat for the same reason, it is a very small piece of the larger Big Bang universe.