Hello! It’s a new year and there’s new stuff to talk about. I figured that to kick this blog off I’d take you through some calculations I did for my research. I would like to give you the reader some idea of what carrying out a typical physics calculation entails. This will take me a few posts so stick with me.
I will begin by telling you about de Sitter space. When I say “space” I mean that it is a space just like how our universe is a “space.” What does it mean from one space to be different from another “space” in physics? Well, certainly there’s simple stuff to start off. For example, a sphere is a different sort of space from a donut in the sense that one cannot be deformed into the other. However, in physics we’re usually thinking more concretely than that. Different spaces have different notions of distance. For example, you could imagine a universe where all the distances stay the same for all time. This is not the case of our universe, as our universe is expanding. Thus the distance between two points is increasing with time. Perhaps “space time” is a better term to use than just “space” in this context, but as everyone else calls it “de Sitter space” and not “de Sitter space time” we will too.
What is de Sitter space? Imagine our 3D world as some sort of 3D sphere. I don’t mean a sphere like a ball with an interior. When physicists or mathematicians use the word “sphere,” they mean the surface such a ball. So the surface of a ball that you’re used to is a 2D sphere, as the surface of something 3D is 2D. It is impossible to really picture a 3D sphere as it is the boundary of a “4D ball.” There is no way to walk out of a 3D sphere just as there is no way to walk off the surface of our earth (with is a 2D sphere). Our universe very well may be, on the largest scale, a 3D sphere like this, although we’re not sure yet. If it were such a 3D sphere, it would be a very very big one.
But that’s not all: de Sitter space is expanding. Well, actually, first it contracts, then it expands. To be specific: the radius of this 3D sphere ‘starts out’ as infinite, then rapidly contracts to some finite radius, then starts expanding again. This expansion is roughly exponential, i.e., very fast.
de Sitter space is not a good model for our universe, as our universe is not expanding exponentially. It did expand exponentially during ‘inflation’ in the moments after the big bang, and it may expand exponentially in the distant future due to dark matter (the jury is still out on that one) but it is not now.
However, this space has very many nice properties and is used to do a lot of very interesting theoretical physics, so that’s what we’re studying for now.