Cosmologists use General Relativity to explain each stage of higher and higher energy particles all way back to a single inflaton or singularity which underwent inflation. Beyond this lies several speculative ideas for what gave rise to the inflaton and inflation. One interesting one is Branes in other dimensions colliding and spawning the inflaton and our space time.
I am not really mathematical hence I do not follow the GR predictions, but I am a believer in the Cosmic Microwave Background Radiation measurements which show a black body spectrum red shifted approximately 1000 times, hence the expansion of our observable space time.
Even if we step over the GR part it is pretty obvious that something very violent and energetic was required to inflate the entire universe especially when the rest of the universe might be 10 to power 30 times the size of the observable universe.
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.
Choatic inflation theory has many possible scaler field functions that may simulate inflation. As Linde pointed out, there are many possibilities.
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.
