What Happens After the Universe Ends?

In conformal cyclic cosmology (CCC for short), the heat death of universe looks a lot like big bang. Essentially once all matter is reduced to photons (and massless particles) there is nothing to track time (or space), light can be understood as being everywhere all at once, thus causing huge amount of energy and with very little entropy. [PBS Spacetime on CCC] ▶ this video

There was a PBS Space Time episode about a year ago that covered what I think is the same recent Penrose idea that you have mentioned [1]. [1] ▶ this video

This dramatic visualization of the timeline for the rest of the universe is well worth a watch to get a feel for what we believe the future of the universe to look like [TIMELAPSE OF THE FUTURE: A Journey to the End of Time] link However, when you get to the end (which is perhaps a little depressing!), I'd recommend learning a bit about what we think could come 'after' this period, where the universe has become so isotropic and homogenous no clocks or measuring systems of any kind can be developed so the universe loses any sense of size or energy – it's been proposed that this creates opportunity for a new universe to exist [What Happens After the Universe Ends?] ▶ this video These are fields of study right on the edge of what's testable by science so it's more fun to think about than it is to have certainty (although Penrose has, debatably, claimed evidence for echos of previous universes visible in the CMB!).

According to CCC and to my understanding, it is sort of the case. The universe has undergone a "scale change" which marks the beginning of a new Epoch. It's explained in this PBS Space Time episode much better: ▶ this video

Argument was a bit more complicated. Basically when all particles are moving at speed of light, time becomes meaningless and you can consider space to be infinitely small. I.e. identical conditions to Big Bang ▶ this video