“What current useful models are there?”
There’s nothing that the mainstream would consider without a lot of appalling name-calling. But let me give you an idea of what to expect:
Once you have given up on certain bad mental habits it takes a while for the mind to shift so as to take in all the implications of a universe without a creation myth. The public servants have the bad habit that things can be created on the instant, rather than by complex processes, and over time. If only it were true around the factory. So they have matter showing up ex-nihilo and expanding outwards at trillions and gazillions of times the speed of light. All embarrassing idiocy of course.
But consider the idea of the photon. It also gets created for no reason, and hot-tails it out of wherever it is at the speed of light.
Supposing you were to put all this nonsense behind you. You face the uncomfortable idea that the matter is here. But since any rational understanding of how it got here, would have it being converted and staying put, then any better theory must have matter being created ON-LOCATION.
We look out at the universe and we see that there is a lot of space and then great accumulations of matter. We pretty much have to accept that the new matter is being created WHERE IT ALREADY IS. And that this is an ongoing process. Otherwise we split time into an age of miracles and an age of the new prosaic world.
Now we would say that the matter is being created where it is but this is really CONVERSION. Since once we get rid of spooky-action-at a distance ……. for gravity to operate all matter in the galaxy must be connected. Since it is manifest that gravity propagates instantaneously and does not wait on light speed.
So we then would see that we could split matter into that matter which is locked into the gravitational web, and that matter which isn’t. And that matter which isn’t has to be presumed the majority by far, and to be barely interactive. So what must be happening is matter must be being converted in moons, planets and stars, from barely interactive matter, to matter that is being brought into the gravitational network and that readily interacts or impinges on other like matter.
20th century physics has banished the natural philosopher and has replaced him with all these maths-boy 101 Raiman types.