I suspect a lot. He has unorthodox views on lots of topics. For one he doesn't seem to believe in the heat death of the Universe. He has some interesting theories in regards to gravitational waves and so on.
> he doesn't seem to believe in the heat death of the Universe
I’m not sure I believe that the heat death of the universe really is the end of all things forever and for all time either, after reading Asimov’s The Last Question and a particularly fantastic manga oneshot adaptation by manga artist Ryul.
If you haven’t read it, I can’t recommend it more highly, and the manga version is a nice addition to the canon. I found a version narrated by the man himself on the Internet Archive, and I also found a fully voice acted audio version from the Drabblecast, also linked below.
One interesting angle I've heard proposed with regard to this is that even post-"heat death", there is no guarantee that local pockets of low entropy will not exist. Indeed - quite the opposite is true: let's say being in a maximum-entropy state requires all particles to assume a fully random distribution (otherwise a potential gradient would exist somewhere, a form of order, and the entropy would not be maximized). Now, take a description of an NxNxN chunk of universal "stuff" (energy, matter, etc). Similar to how we can find every string of digits in Pi if we look long enough (each given substring is equal to the search string with probability 1/10^N, N is length of string), we should be able to find every possible chunk in the maximum-entropy universe, with the probability for any given chunk matching being 1/M^N^3, (M is the universal "base", how many options a given location has for what it can be in the encoding we are using).
Long story short, assuming an infinite universe post-"heat death", we'd expect to be able to find every possible arrangement of particles represented at some location, even very complex ones such as the entire universal state we observe today.
I've heard these theoretical ideas advanced also, perhaps in writings by Richard Dawkins but I'm not sure; iirc the idea is loosely related to the concept of quantum foam but I may be mistaken.
> Quantum foam or spacetime foam is a theoretical quantum fluctuation of spacetime on very small scales due to quantum mechanics. The theory predicts that at these small scales, particles of matter and antimatter are constantly created and destroyed. These subatomic objects are called virtual particles. The idea was devised by John Wheeler in 1955.
It's important to remember though that these words, i.e. "virtual particles" are just words used to convey a-priori what are purely mathematical constructs. It in no way is declaring that such things are tangible instances (e.g. detectable in a cloud chamber or through other empirical means.)
These future states may as well be parallel universes, however: there's no real way for them to interact with each other across the vast time and space of maximal entropy.