I am a Ph.D. Physicist but I'm not a cosmologist. Nevertheless, this subject fascinates me so I have kept abreast of the current research.

These are very interesting ideas. Some like "Cosmic Inflation" have become mainstream views. (Disclaimer: I accept it as almost certainly true.) Cosmic Inflation is certainly not "proven" but it is supported rather strongly by the indirect evidence from the Cosmic Microwave Background observations. It will be hard to ever have a more direct "proof," or test, of the idea of Cosmic Inflation until and unless we can directly observe primordial gravitational waves. We have not been able to do that yet and we may never have that capability.

There are currently two big schools of thought in Theoretical Physics as many here know. Those are String Theory and Loop Quantum Gravity. Both are attractive theories for different reasons. Interestingly, Loop Quantum Gravity predits a cyclic universe with a Big Bounce as a primary component. I lean more towards String Theory but definitely remain open to some of the more compelling ideas of Loop Quantum Gravity.

The astronomer Edwin Hubble hypothesized that the universe is "unbounded in space and time".
Really big and really old.

The Big Bang and inflation have always seemed implausible to me. Hard or impossible to disprove, of course, and even possibly correct. But I prefer alternatives.

Very cool theory