therefore the statement " all matter eventually separates in this way" , strictly speaking, seems false since gravity and electromagnetism overcome expansion at local levels.
Yeah, both are right in context. It's just like saying "gravity doesn't make objects fall at the same speed". It actually does make them fall at the same speed...but if you include other relevant forces, the overall effect is different.
I thought the Big Crunch was disproven because we found that the expansion of the Universe is accelerating. Dark Energy wins over Dark Matter...forever.
More likely than not, the Big Crunch will not happen. From Wikipedia:
"Recent experimental evidence (namely the observation of distant supernovae as standard candles, and the well-resolved mapping of the cosmic microwave background) has led to speculation that the expansion of the universe is not being slowed down by gravity but rather accelerating. However, since the nature of the dark energy that is postulated to drive the acceleration is unknown, it is still possible (though not observationally supported as of today) that it might eventually reverse its developmental path and cause a collapse."
It was my understanding that this is true from our perspective in time right now, but the Big Crunch could still be plausible if the universe turns out to be young enough (which it seems like it is) that not all the fusion fuel has been exhausted. Once it is, we'll have big clouds of nuclear waste interspersed between black holes, and perhaps in this environment the Big Crunch could still occur.
I think another question for the Big Crunch is what type of "fuel" is needed to create an exothermic fusion reaction comparable to the Big Bang? For example, the sun compresses hydrogen to produce helium and release massive energy. Black holes are undoubtedly compressing helium enough to make Beryllium, but this doesn't seem to release any energy that can escape the gravity that created the pressure required in the first place. So for the Big Crunch - Big Bang cycle to hold up, what type of matter (and how much of it) has be be compressed (and is gravity the only force that's compressing it) to the point where some type of "fusion" reaction produces enough energy to escape the compression forces?
> perhaps in this environment the Big Crunch could still occur.
No, it couldn't. The nuclear waste will still have the same average energy density, on the scale of the universe as a whole, as the unexhausted fusion fuel does now. We know that energy density is too small now to make the universe recollapse, so the same must be true any time in the future.
> what type of "fuel" is needed to create an exothermic fusion reaction comparable to the Big Bang?
The Big Bang was not an exothermic fusion reaction. Our current best model is that the Big Bang was caused by a very large energy density being transferred from the inflaton field (the field that drove inflation in the very early universe) to the various fields in the Standard Model of particle physics (electrons, quarks, photons, etc.). This "reheating" created the hot, dense, rapidly expanding state that we refer to as the Big Bang.
FYI, gravity might eventually overcome spatial expansion on a cosmic scale. But we don't know. https://en.wikipedia.org/wiki/Big_Crunch