I agree with all your points here. It seems like the "standard picture of inflation" curve is the crux of everything, and is referred to repeatedly. But he doesn't even define the axes well. (I agree with your complaint about the axes - he says the y-axis is energy, but the x-axis is specifically in units of energy).
I'm unclear on one apparently critical point that maybe someone can clarify. I see what he's saying that the universe dominated by vacuum energy expands much more quickly than one dominated by radiation or matter. But does this mean that it's expanding faster the the speed of light? It seems to me that he's saying the multiverse happens because there are these pockets within the multiverse of slow expansion (an individual universe within the "well") and fast expansion in between, right? But then the only way those pockets could not be observable between each other is if the "fast expansion" region is faster than light. Why does the fact the the expansion doesn't slow down in a vacuum dominated universe mean that certain parts of the universe are out of reach of other parts. Is gravity the culprit here?
Part of this comes down to his equation(s):
size ~ t^n, where n = 2/3, 1/2, or 1
First of all, what is "size"? Volume? Length? Area?
Second, and most importantly, why isn't that expansion rate linear in time for everything. What is it about the physics that makes a matter dominated universe expand differently than a radiation-dominated universe? Is that easy to explain? And if so, that's crucial for my understanding here.
Something that's never been clear to me in the expanding universe model is why the expansion of the universe results in red-shifting of light and shifting of the CMB to the microwave region. Can someone explain this? If the expansion is of space itself, which I interpret as the "grid" upon which matter/radiation exists, how does light or anything else know that the grid is expanding? In the silly picture in my head, I'm thinking that I won't know that my ruler is changing length since I'm changing length with it, just like how person A moving at near the speed of light relative to person B doesn't know that the space that they're in has "shrunk" according to person B. In the model of the expanding balloon with ants on the surface, how do the ants know that the expansion is occurring? If I were one of the ants, I'd draw a grid around me out to the next nearest ant. As the balloon (universe) expands, the grid would expand with it, so I would have no idea that the next ant is getting further away. Why is it different in the universe expanding? Is it just radiation that knows of the expansion? I'm clearly missing an important concept, but I don't know what it is.