One idea that captures my imagination is the concept of cyclic inflation – a framework that combines cosmic inflation with the notion of cyclic collapse and expansion, or bounces.
This captivating idea, conceived by former postdoctoral researcher Dr Tirthabir Biswas and myself, suggests that the Universe undergoes infinite cycles of collapse and expansion.
Here's a link to the good professor's paper for those interested. As others have already pointed out, cyclic universe as an idea is not new -- the paper itself cited refs 11-19 as prior art, the oldest of which dated back to 1931.
The claim the good professor is trying to make is somewhat subtle for any lay person skimming through the article: the novelty of their idea is not cyclicity itself, but rather to combine cyclicity and inflation. To be honest, as a lay person I would have thought a cycle would consist of an inflationary period and a deflationary period, so forgive me for not seeing the point! The following technical statement from the paper perhaps makes more sense:
Thus although cyclic and inflationary models are not mutually exclusive, it is natural to try to attempt to replace inflation altogether with “cyclicity”. In this paper, however, we take a slightly different approach, by exploring whether by embedding inflation in a cyclic universe setting, some of it’s problems viz. (i-iv) can be alleviated. Our main idea is to merge inflation with cyclic cosmology where the universe undergoes an infinite number of cycles before bouncing into a final power-law inflationary phase.
I think the better way to say this is that not only do you get inflation (and deflation) for free within each cycle, but the sequence of cycles is itself inflating -- a larger scale inflation modulated by a smaller scale periodic function if you will.
The question now is, of course, is there a "first cycle", and what happened before it. Why stop there and not have some meta-cycles? That would bring the whole business to a full circle.