Ok, so I told you about wave packets and how they expand and why they’re important. So now what happens to wave packets in de Sitter space? This was a question that I made for myself in order to get a better grip on what de Sitter space is all about. Do momentum states separate nicely like they do in flat space?
The answer, simply, is no, they don’t.
As space starts expanding exponentially quickly, points once close to each other soon grow incredibly far apart. Whereas in a non expanding universe particles are able to move farther and farther apart, in a rapidly expanding universe they get ‘stuck’ and ‘freeze,’ so the momentum of the particle becomes less and less important compared to the expansion of the universe.
Intuitively, what this means is that particles aren’t able to really `separate’ from each other, they just get stuck. There isn’t really a notion of particles moving at infinite times.
So how does one calculate something like that?
Well, the first step, and I think the hardest step, is setting up a calculation. Physics is a network of equations and interpretations between these equations. If you’re curious about some physical process and want to investigate it, you have to use what you know to follow the right steps and set up the right formulas to calculate.
The second part entails using all of your acquired calculation skills from taking classes and doing homework to rewrite your formula in a more useful form that admits a simple interpretation. Usually this requires using some justified approximations. Most physical equations are just good approximations that get all of the essence of the physics without carrying a lot of extra baggage.
This is especially true in quantum mechanics / quantum field theory. Exact solutions are almost always hopeless, but luckily there’s a very large toolkit of approximation schemes that are a pain to learn but vital to learn.