Can gradual expansion creates a smooth, uniform, and flat universe. Is it possible that the early universe was a gradual expansion instead of a very rapid and short expansion (inflation)?
The issue is to solve the horizon problem: if different part of the universe are not causally connected then it is impossible to understand how they would have interacted to reach an equilibrium with a smooth energy/matter distribution. Inflation was invented to specifically solve this issue and it does that quite well judging by the very good fit of the theory to the observed Cosmic Microwave Background Radition (CMBR) and galaxy cluster distribution throughout the universe.
However, alternatives have been proposed. One of the most popular a few years back was variable speed of light (VSL): faster in the early universe, fast enough to solve the horizon problem. But it is hard to flesh that into a consistent theory. I'll redirect you to Wikipedia. I may add more later about the issues with this idea.