expansion - How can an infinite universe expand?

I understand the expansion of the universe as actually an increase in the ratio of space to matter. Is this a correct understanding?

It isn't wrong. The ratio is increasing. But it isn't a "correct understanding". It's merely an observation of one of the results of the expansion of space.

If the universe is infinite how can it expand?

I don't know. Nor do I know how big bang cosmology can be reconciled to an infinite universe. If you look around on the internet, you can find articles like this which say this:

"The linear dimensions of the early universe increases during this period of a tiny fraction of a second by a factor of at least 10$^{26}$ to around 10 centimetres (about the size of a grapefruit)".

However in 2013 results from the WMAP mission appeared to confirm that space is flat. Then a non-sequitur crept in. See this article and pay careful attention to this:

"We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe."

That's a massive error. It absolutely doesn't suggest that the universe is infinite in extent. Or that the Universe is much larger than the volume we can directly observe. But this myth has legs, and people repeat it ad-infinitum, even though they can't explain how it fits in with Big Bang cosmology. What you tend to hear is that the observable universe was the size of a grapefruit, but it absolutely doesn't satisfy. Moreover there's a dreadful flaw lurking in the shadows. Take a look at the stress-energy-momentum tensor, and note the energy-pressure diagonal. A gravitational field is something like a spatial pressure gradient, and you can think of space as having an innate "pressure". So you can reason that the universe must expand. As to why Einstein didn't, I just don't know. But anyway, for an analogy, squeeze a stress-ball down in your fist, and let go. It expands because of the pressure. However if that material was infinite in extent, the pressure is counter-balanced at all locations. So it can't expand. In similar vein, in my opinion, an infinite universe can't expand.

People claim the universe must be infinite because of the cosmological principle. But this is merely an assumption. There's an assumption that the universe is homogeneous and isotropic, but this isn't fact. You cannot use it to make sweeping claims about an infinite universe that was always infinite. For all we know some observer 50 billion light years away might be looking up at the night sky wondering why half of it is black. Or a mirror-image of the other. Or some kind of edge.

It is said that in days gone by, people could not conceive of a world that was curved. They could only conceive of a world with an edge. Nowadays I rather fancy that there are some people who cannot conceive of a world that is not curved. They cannot conceive of a world with an edge.

Edit:

See The Foundation of the General Theory of Relativity: "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". Energy is the source of the stress-energy tensor. Matter is only a source because of the energy-content. Also see Inhomogeneous and interacting vacuum energy which refers to spatial energy. An interesting read is the article Universe 156 billion light-years wide
featuring Neil Cornish. This isn't entirely accurate, but the compound interest and the hall of mirrors concepts are of interest. As for the non-sequitur, see this interview with Joseph Silk:

"We do not know whether the Universe is finite or not."

I hope nobody will argue with that. Reading on:

"To give you an example, imagine the geometry of the Universe in two dimensions as a plane. It is flat, and a plane is normally infinite. But you can take a sheet of paper [an 'infinite' sheet of paper] and you can roll it up and make a cylinder, and you can roll the cylinder again and make a torus [like the shape of a doughnut]. The surface of the torus is also spatially flat, but it is finite".

This is akin to the old Asteroids game. But the Planck mission found no evidence of any torus. Reading on further:

"So you have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat."

I dispute that. There is a third possibility. A flat finite universe with no intrinsic curvature. If anybody can cite some reliable sources that support the assertion that a flat universe must be infinite, I'd like to see them.