If you're interested in this area I strongly recommend you rea Alan Guth's book The Inflationary Universe. It's well written and easy to understand even for non-specialists.
In Guth's original model there was a postulated symmetry breaking transition when the strong force separated from the electroweak force. If this is a first order transition then it is possible to get supercooling so the temperature of the universe fell to below where the symmetry breaking would normally occur. When this happens it's easy to show (see Guth's book) that the supercooled state forms a false vacuum that behaves like a negative pressure and causes exponential expansion. This produces inflation, and the universe carries on inflating until the false vacuum decays and the symmetry breaking finally happens.
However it was quickly realised that this simple model suffers from the so called graceful exit problem so it cannot be a good description of what actually happened.
Much overheating of brain cells later the proponents of inflation have given up trying to work out exactly what caused inflation and they just specify that there was an inflaton field without specifying its physical origin. Googling will find you many, many theories on what the inflaton field may be, but no one idea has proved compelling and the honest admission is that right now we simply don't know what caused inflation.
It may be that the original idea has some merit and that the symmetry breaking that split off the strong force is at least related to the inflaton field, though not in the simple way that Guth originally suggested. However, even if this was the case it would be wrong to say the strong force caused inflation. Rather the reverse really, as the strong force appeared only after symmetry breaking and that would be the point at which inflation stopped.