To al-amiyr:
Although it is very important for scientists to ask and formulate the questions and then formulate hypothesis, and make prediction, eventually real science comes down to observation, to verify - or even more importantly, to refute - the hypothesis.
Observation can come in many forms, and not necessarily what we can only see with our naked eyes.
- Instrument or equipment can be used to detect signs, signature or whatever phenomena are out there, which our eyes can't see, our ears can't hear, or our touch can't touch. Even though we may see, hear or touch something, we can't actually quantify (measure) what we see, hear or touch, that's why we can use technology to take those measurements.
- Observation can come from experiment or testing, where we can measure or quantify in some ways.
- Observation can also come from evidence. Evidence is vital in science, and it allow us to verify or to refute a hypothesis, or allow us to formulate new theory, modify existing theory or discard obsolete theory. It is important to find independent evidence to verify or confirm if the first evidence is not an error or fluke (by just happenstance). Note that evidences can also be tested.
The reason why I bring this all up (about scientific hypothesis, observation and evidence) is that the cosmology of how the universe would end, it is purely theoretical, and conjectures.
Theoretical physics - or more precisely theoretical astrophysics - rely more on logic (abstraction) and mathematics (mathematical models) - than on evidences - to explain a phenomena.
How the universe ends, is far harder to predict.
Big Bang is no longer theoretical, for we have evidences to support that the universe has expanded from singularity. However, what was before the Big Bang, is also theoretical, and conjectures, mainly because we don't have the technology (yet) to see further back in time. We don't know what this singularity is, except that it was very dense and very hot, before the expansion (Big Bang) began.
Your Qur'anic Cosmological Model is based on the cyclical (or oscillatory universe) cosmological model, often called the Big Bounce.
The Big Bounce mean the universe will expand, contract, expand again, contract again...possibly in infinite number of times. So there could be Big Bang, Big Crunch, Big Bang (our universe), Big Crunch.
There are no evidences to support the Big Crunch or your Big Bounce model, mainly because we still see evidences that the universe is still expanding, and it is accelerating in its expansion, so the most likely scenario for the end of the universe is the Big Freeze.
The Big Freeze is where everything in the universe (galaxies, stars) will continuously expand.
Whatever the scenario with regards to the universe, wouldn't really matter to us, because this solar system (especially our Earth) will not be there when the time come.
Our Sun will eventually run out of hydrogen fuel. Our Sun will not become a Black Hole or neutron star because the Sun is not massive enough. Nor will it explode like in the supernova, because Sun still doesn't have enough mass. Our Sun's fate is that of Red Giant before becoming White Dwarf.
As the hydrogen gradually become depleted, the Sun will expand in size. Perhaps a billion or 2 billion years before become a Red Giant, the Earth's atmospheres will burn away, and every drop of water would dry up, and this Earth will be like what Venus is now. By the time Sun become Red Giant, it will have swallowed up Earth.
The Sun will become fully a Red Giant in 5 to 6 billion of years from now. But even that, that's still not the very end of the Sun.
It will become planetary nebula, where materials from the outer layers of the Red Giant will be ejected. And lastly, when every layers are ejected, until the core remain, the planetary nebula will become a White Dwarf (8 billion years from now).
We know this is the fate our sun (and solar system), because the Sun is classified as a yellow dwarf (Class G), a star with medium mass (or perhaps low mass, I don't remember). It is the mass that determine if the star become a white dwarf, supernova or black hole.
No life would be on Earth when the Red Giant swallow up the Earth. And the Earth would have cease to exist billion of years when the universe end.