"The accelerating expansion of the universe requires an explanation, and thus far none is even being entertained as a mainstream idea."
My theory is it's accelerating because of gravity.
The pre-big bang singularity was a black hole that contained all of the matter in our universe. It had an event horizon and outside that event horizon was matter going on about its business, without a care in the world, the same way matter in our universe goes about its business every day as long as it's beyond any black hole's even horizon.
So that matter, which is so much greater in volume than what's in our universe, has its force of gravity acting on us, everywhere, all the time, pretty much a constant though there are minor fluctuations in distribution as the matter outside our universe moves around just as it does inside.
Since the force of gravity between two objects increases at a greater than linear rate the closer they get to each other, as the outer perimeter of our universe approaches the inner boundary of the outerverse, multiverse, omniverse, megaverse, or whatever you want to call it, naturally both groups of matter will accelerate their approach to one another until they collide, intermingle, and we again join with the matter outside of universe in eventual equilibrium. As long as we avoid getting sucked into another pre-big bang singularity. It's said that there is a star going super-nova every two seconds in our universe. In the outerverse, there may be a pre-big bang singularity (PBBS, I pronounce it PiBBS) reaching critical mass and temperature and exploding into a new universe every two seconds as well, kind of a universal, or omniversal as it were, constant. Those are the heartbeats of God.
What we see, all that we'll ever see or know, is the tiniest fraction of all that's out there. We're less than frogs looking up out of a well. All the matter in our universe is to all the matter in the outerverse as a neutrino is in mass to the PiBBS that birthed us.
One thing that I'll mention about proving God, as nice as it would be if we could, is that it kind of misses the whole point of faith.