So, in the meantime gravitational waves have been detected by LIGO. Does this then disqualify this cyclical model?

Yes, inflationary theory seems to be explaining the emergence of the multiverse rather than the expansion of our particular Universe.

Not sure about this, to me it seems that the apparent effect of motion on space is the contraction of space in the direction of motion. To me it’s more like an optical illusion, because the actual length of, for example, the train measured by someone on the train is the actual length of the train, everything else is an optical illusion due to motion, so in a sense the special relativity calculates the optical illusion of the contraction of the moving train.

Yes, I understand the reasoning I just wish I could see the mathematics of it but I guess the gamma factor is used to prove the theory.

The Sun rises in the East and sets in the West with a circadian cycle. Also, every night stars/planets rise in the East and set in the West. This is due to Earth spinning not the distant stars actually moving with respect to the Earth, it’s the Earth that is spinning on its axis anti-clockwise.

The fact that we only understand 5% of what the Universe is made of, doesn’t mean that all our accumulated knowledge of astrophysics/cosmology only amounts to 5% of what there is to know, as in quantitive terms, for example, dark matter and dark energy are only two concepts, albeit very important concepts, which if discovered, would allow us to understand approx 100% of what the Universe is made of. So in quantitive terms, it may be that we already understand 98% of what there is to know, if dark matter and energy were the only outstanding issues in cosmology, which they are not.