The release of energy from the symmetry break that differentiated the strong force from the electroweak force caused the inflation. The currently accelerating expansion, as you've already been informed, is due to other reasons. And, of course the currently accelerated expansion is treaded differently from the Big Bang inflation, because they are ultimately separate phenomena. There is not even the most remotely slightest contradiction in that.
More problematically, cooling is a transfer of information, violating Relativity during that stage where "space" alledgedly expanded in between matter at speeds vastly higher than C (i.e. "from about 10-36 seconds until about 10-32 seconds.").
This problem exists only in your fantasy world, but in any case, what part of 'quantum effects overwhelm relativity in the early universe' didn't you understand?
"This problem exists only in your fantasy world, but in any case, what part of 'quantum effects overwhelm relativity in the early universe' didn't you understand?"- AntiGuv
Except, you don't even have Quantum Effects in such an early universe, just a "unified field." You've got to pretend that there is no Gravity, no independent Strong Force, no independent Weak Force, no independent electromagnetic force.
Then you've got to pretend that there is no Relativity (ooops, I mean, that relativity is "overwhelmed"). Then you've got to pretend that a "superdramatic" explosion hyper-accelerated Space, but not matter, vastly faster than C due to cooling that couldn't even happen prior to said explosion (because space hadn't expanded prior to said explosion event).
And that's just the Inflationary Era.
After that point, you've got to shift gears to pretend that the current ever-increasing rate of universal expansion is due to entirely different, though currently completely unknown (dark energy is a guess with no lab or physical support), processes.
You can make post after post about me being ignorant, arrogant, whatever, that still won't change the fact that the Big Bang Emperor has no clothes as itemized above.