[Physicist]

Above you seem to be saying that there is still some sensitivity to initial values even with inflation. Is that correct?

No, the point is that Inflation pulls the density to the critical value, so that by the time the Inflationary epoch is over, the density is pegged to it.

Part of your confusion is caused by my sloppy wording, "close to the Big Bang". The end of the Inflationary epoch is much closer to the Big Bang than the energy explored by the LHC. The energy density at the time of inflation is comparable to the grand unification scale, way up there.

[man of Yosemite]

Since you seem to be a real scientist, I'll share an incident that happened several decades ago that has left me wondering all these years. I was in the Sierra Nevada Mountains in the vicinity of Mammoth Lakes during the third week in July. My brother and I were lying on our backs looking up at the stars when one of them seemed to appear to pop; the light just rushed away in all directions in a split second. I would compare it to the popping of a soap bubble in the air. I have never mentioned it to a astronomer, but if we saw a star explode it would be provable, the missing star would be on someone's chart. I'm not sure that is how these things happen, but we certainly saw something.