What gave rise to cosmic inflation of the early Universe?
We don't know yet. When we discover precisely what inflation is, if we're very lucky, perhaps that will come along with a specific model for how inflation began as well. In the mean time, theorists have come up with a great many ideas, but we don't yet have experiments to distinguish between them.What gave rise to cosmic inflation of the early Universe?
Well, Chaotic inflation merely proposes that the potential energy is quadratic. The problem is, near enough the minimum, almost any potential energy will be quadratic, so if we detect chaotic inflation, and no deviation from it, then we will obtain basically zero information about what caused inflation. Unfortunately, because chaotic inflation is so generic, it is the most likely.Choatic inflation theory has many possible scaler field functions that may simulate inflation. As Linde pointed out, there are many possibilities.