This isn't a new idea. It's been kicking around for some time (at least two decades), rather hard to prove/disprove since there's no currently known mechanism, even theoretical, for observing what might have happened befoee the big bang.
That isn't entirely true. As the article discusses, under the proposed conformal cyclic cosmology, gravitational waves would leave a lasting effect visible between aeons. This effect would be visible in the CMB, and some researchers (including Penrose) claim to have found such a signature in their analysis of the CMB. The validity of their analysis is still in dispute (because detecting such a signal from the noise of the CMB is a very hard problem), but in principle the signal would be there if CCC is correct.
I have a really hard time understanding how gravity waves would survive the Big Crunches. Probably my failure to understand comes from how I think of space.
If all matter is re-crunched into a "singularity," then no space remains? Right? Or time either?
Where do these residual gravity waves exist? If the void of nothingness? That seems wrong.
I guess based on the article that the theory proposes that not everything is re-crunched (dubious?) but that some stuff remains in the universe (dead black holes are somehow not re-crunched?), and therefore space and time do not cease to exist between Bangs and Crunches?
I don't know. I just don't really understand, which is fine as I am a brain scientist not a physicist.