Repeated Big Bangs is not in question. At least certainly not with eternally existent Universe.
Those initiaing moments for a new phase of eternally existent Universe. The Big Bang, occur from already existing Universe, in another phase of existence. Entropic heat death. Understand that first. More below.
Ive presented various scenarios around here over the years.
1} early ones stem from Euclidean 4-fold Vector Equilibrium{ VE } --has a spherical version also-- and the associated primary 87 { - 14 congruent/redundant = 73 primaries } great circles,
...a spread out version of the above with many 4-fold VE and 5-fold icosa...
....1a} entropic heat death of 4-fold VE physical reality, --via contraction to flat, becomes ultra-large, ultra-flat { longest frequency } photon with 5-fold icosahedra remaining on each side if not overlapping the ultra-flat 4-fold VE. There is more to the story
2} similar to above except the 2D great circles have become my primary 73, dual invaginated space and time horn tori via every particles of Universe
...Gravity is outer positive surface, and Dark Energy is inner negative surface. Physical reality inside/internal to the torus.
We do not see the Gravity or Dark Energy because they are not quantized as observed time. We only see discreet particles of reality that, are associated with sine-wave pattern ^v^v^
Scenario 1:
3} the space and time tori follow same idea as presented above for Euclidean or spherical VE and icosa at entropic heat death, --more time needed to get in to all the details once again.
...3a} the most recent scenario is about our pereceptions of expanding Universe are incorrect and what is happening is that reality { ^v^v^ }, ---inside each particle of Universe---, is synchronistically moving toward ---over zillions of years-- either outer Gr. or inner DE.
As the reality gets to the outer or inner surface, it is transported around to pop back in on the diametric opposite side. The normal for zillions of years.
Whats unormal is that sine-wave of reality accumulating --and flattening out ' entropic heat deat '-- inside each particle, so that when it gets too outer or inner, there is going be a massive influx of the sine-wave or reality, that travels around the surface and pops back in.
Dark Inflation occurs a short time as enough of the reality accumulates to inflate/expand and create enough energy to have all kinds of energetic transformations aka Big Bang. This story is a bit complex and I certainly dont have any abstract or geometric graphics to develop it much more.
In this latter cause Universe is not truly expanding or if is, not of significant amount, Rather it is pereceptions --even via our instruments-- that mislead us to thing the Universe is getting larger.
If we stop to think about using logical common sense critical thinking. Is the Universe like a rubber band that expands and contracts?
Entropic heat death is cooling off, not a getting hotter. Metal and other substances expand when getting hotter.
Again, my viewpoint is that, there is finite occupied space of Universe, and if Universe is truly expanding, what is filling the seemingly empty space that would be inside and expanding Universe.
If the VE as reality is contracting to become ultra-large and ultra-flat, it expands into a a seemingly flat area of a triangle or circle if we start with a spherical VE.
So no truly empty space is required to fill in space, as the finite VE { as reality } is just transformed from spherical/polyhedral to flatten area.
That still leaves ideas about the role of the 5-fold icosahedra. In my standard model,teh 5-old icosa is pattering for the bosonic forces of Universe and yes they are reality, yet in the top of this page scenario, the icosa outer i..e on each side tangent to over overlapping to the central ultra-flatten VE.
In my early scenarios, all that exists is encoded on the spherical surface of the icosahedra.
in later scenarios, I would now have these outer space and time tori. So for my early scenarios, it would take me more to develop a logical common sense critical thinking understanding of what occurs. Once that is done i could try to explain.