Cyclical Universe based on Big Rip Scenario
I propose to offer a few mass distribution diagrams to demonstrate why the portion of the universe we are in is cyclical.
First
To describe the beginning based on the last big rip starting our section of the universe requires that the trends to infinity correspond. This occurs first at derivation of four.
Second the initial mass distribution
Based on our section of the universe drawn in the thinning would occur most at the edge of the metric expansion. Surface of the sphere being x^2 and volume being x^3.
I could include a diagram of filaments of density but as you already would have seen them they are the best description of Professor Stephen Hawking's "Spaghetti over the event horizon" possible.