[pdonis]

> Can anyone explain the definition of big bang that they're using here?

They're using "Big Bang" to mean the hot, dense, rapidly expanding state that is the earliest state of the universe for which we have good evidence. In models with inflation, this state occurs at the end of inflation, when "reheating" transfers all the energy stored in the inflaton field to the Standard Model fields (quarks, leptons, and radiation).

This is actually the standard definition of "Big Bang" used in cosmology, but unfortunately pop science books and articles still use "Big Bang" to mean "the initial singularity". We don't even know if there was an initial singularity (in eternal inflation models, for example, there isn't one).