I know that in our particular case the inflaton field expanded the volume of the universe while simultaneously maintaining a mass-energy density close to the critical density all the while, thus the flatness.
But why that number? Why didn't the inflaton field maintain a density which would have caused some other kind of curvature instead? I thought inflation was supposed to solve the fine tuning problem but I still run into the problem.
Basically, what makes inflation "choose" which energy density to maintain? And if it always picks the critical density (for flat curvature), why is that?