We’re reasonably sure the universe as a whole is infinite. Whether or not you want to accept that as a valid size is up to you, but I’d recommend defining “size” to include ordinals.
I don't know what that means. As a kid, my notion was that spacetime was "infinite", that galaxies floated in spacetime, and were moving apart. Gradually I became (a bit) more comfortable with the notion that spacetime is somehow created by "stuff", and that a location in spacetime that has never seen a photon isn't a location in spacetime at all.
A lot of commenters here seem to be saying that spacetime was always infinite; they claim that the universe that used to be the size of an apple is now the whole observable universe. The implication is that there was plenty of stuff beyond the "apple-peel", but that all that external stuff has never had a chance to interact in any way with the interior of the apple.
I don't know how to grok that. There's plenty of stuff that used to be part of the apple that isn't observable; presumably there was some location within the apple that later became the Milky Way, and any photon departing that location 13.8B years ago will never be observable. Arguably, more than half of what used to be the apple will never be observable.
The story I've been sold is that it's not that stuff is moving apart, but that spacetime is expanding. I can visualize 3D space expanding; one moment it's the size of an apple, a few moments later it's the size of a grapefruit. But what does it mean for time to expand? The very idea of expansion is of a thing that grows relative to time. Spacetime is the idea of everything, everywhere, all at once. It's not an anthropocentric notion; it doesn't depend on observers, and I fail to see how spacetime can be considered to be evolving in time.
Neither is especially accurate. Spacetime is not a substance, and it's not created or destroyed. It's the thing physics happens on, for lack of a better non-mathematical description.
> But what does it mean for time to expand? The very idea of expansion is of a thing that grows relative to time.
Same thing as for space: that component of the metric - the shape of spacetime - is an increasing function of coordinate time. But you can always pick a coordinate system where only the spatial components are expanding. It's not physically meaningful either way. The metric is the real object.