We need to differentiate between the universe and spacetime.
I appreciate that spacetime is curved by matter, hence gravity, yet despite this, there is still the discussion as to whether the universe is flat or curved, as per this article: Cosmological crisis: We don't know if the universe is round or flat | New Scientist
However, it makes sense to present the Universe as both flat and curved, depending on whether we are looking at it three or four dimensionally.
The following diagram presents the universe in the fourth dimension (temporal) only, with the (three) spatial dimensions presented as a flat surface, i.e. the leading edge of this cone (blue grid) is the universe as we experience it right now, with all matter sitting on this plane (the diagram I've stolen from the internet is is misleading, as it shows matter sitting behind the leading edge, presented as some form of historical progression):
However when we apply matter and hence gravity to the leading edge of this cone, we experience spacetime as "closed" or spherical:
This makes perfect sense, as when we show a map of the Earth in a book, we flatten its three dimensions into two.
However, I'm talking about the curvature of spacetime in the fourth dimension only. When we 'flatten out' the blue grid of the sphere, would it be completely flat, or would it be slightly curved? The mathematics of trigonometry carried out on the Cosmic Microwave Background suggest that the universe is 'flat', as discussed within this article: How do we know the universe is flat? Discovering the topology of the universe (phys.org)
According to the mathematics - it appears to be flat (Quote: astronomers estimate that the universe must have been flat to 1 part within 1×1057 parts.).
I don't dispute the accuracy of the mathematics above, yet I remain unconvinced that the universe is completely 'flat'.
I have created a model that looks at a four dimensional 'multiverse' theory, placing our universe's Big Bang on a much longer "arrow of time" timeline, preceded by an earlier Big Bang that may account for the forces of Dark Matter and Dark Energy on our universe. Please find the model below:
My model makes the following assertions:
Our Big Bang was secondary to a previous Big Bang (perhaps the original, perhaps just preceding).
The preceding Big Bang created spherical spacetime (perhaps within a vacuum), originating from a singularity.
Our (secondary) Big Bang happened / is happening across the fabric of spacetime created by the preceding Big Bang.
Our Big Bang either creates a secondary / 'child' spacetime continuum, or simply generates matter that interacts with the spacetime generated from the preceding Big Bang
The interaction of the primary and secondary fabrics of spacetime (from the two Big Bangs) account for the "gravity" that is current theorised by the concept of Dark Matter, i.e. our universe is 'held together' via the fabric of spacetime generated by the previous Big Bang / multiverse
The ongoing 'expansion' of spacetime from the preceding Big Bang accounts for the force of Dark Energy on our Universe. The growth of our universe continues to accelerate due to two factors, namely the secondary Big Bang (i.e. the birth of our Universe) plus the ongoing expansion of the spacetime continuum/ multiverse from the preceding Big Bang.
These ‘paired’ Big Bangs may be cyclical – any future ‘imbalance’ between the forces in play could create the ‘splintering’ of our universe into ‘pockets’ of matter & spacetime, which would eventually succumb to the power of supermassive blackholes, creating gravitational singularities that would power the birth of new Universes within each ‘pocket’
To your other points:
"There isn't a way anybody could possibly know anything about a time before the Big Bang. Our best maths fizzle out before we can get all the way back to t=0, where the heat and densities destroy any information we might be able to get." - If we look at the problem a different way.... Using the model above, if we understand the (albeit very slight) curvature of our 4th dimensional universe - 1 part within 1×1057 parts across an observable universe of 84 billion light years, then would would be able to estimate the birth of the (theoretical) big bang that proceeded ours.
"But the dimensions would still be there without the matter, so it's not a natural extension of them" - Time would exist without matter, but space wouldn't. With matter there would be no gravity. Without gravity, space (the spatial dimensions) would not exist.
A model is the maths a theory is based on. Do you have a model, or want help with a model? I need a mathematician to help my prove/ disprove my theory above - can you help?
You may have some gaps in your science you've filled in with popular misconceptions. It happens a lot when smart people get hold of parts of the puzzle, become hooked, and then make up the rest. I'm sure it makes perfect sense to you, now you have to explain it so peers can understand it. - I have enormous gaps in my knowledge. I am a strategic thinker with a dangerously small amount of information. I know that my ideas are based upon 'cobbled-together' pieces of theory, some which are proven and some which are not. There is no tie-together between special relativity and quantum physics within this model - it is purely mechanical, yet could still work.
Can you help me?