Inflation: fast or slow?

As many might be aware, the cosmology community is expecting a little later today to hear of what may be the first hints of a measurement of primordial B-mode polarisation of the CMB. This, as you can read elsewhere is indicative of gravitational waves originating from cosmic inflation. It’s not surprising then that inflation is very much being talked about.

Andrew Pontzen caught my attention this morning on Twitter when he said:

You should definitely click through to here right now where he makes an excellent explanation of inflation, and why he feels it shouldn’t be described as ‘fast’ or ‘rapid’ (if you are reading this and happen to be Andrew, you can probably skip this step). I think it’s a very well argued case, although I don’t think it has me fully convinced. This blog post is in part an effort to get my thoughts straight on it.

First off, I’ll say right out of the bag that it is one of my pet peeves to talk about things like inflation being ‘faster than light’ (coincidentally, another one is calling gravitational waves ‘gravity waves’, which are something else less peculiar, but arguably more photogenic) – cosmic expansion has the wrong units to be compared to the speed of light for one thing, and at no point does anything either in inflation, or in late-time expansion ever overtake light.

I’ll also say that at no point do I disagree on any of the facts with Andrew, merely on how they might best be described – in this manner it’s not unlike numerous but physically unimportant debates about whether space expands. Cosmologists frequently like to get their knickers in a twist about this sort of thing, while agreeing 100% on all observational predictions and facts, and merely argue about how best to explain to other people what we’re all going on about. I note on this front that John Peacock has, as linked by Andrew, a useful note on this topic much as he does with his well-known ‘A diatribe on expanding space’.

With all that said, let’s look at the question – is inflation a period of slow or rapid expansion? Well, arguably it’s not even a period of accelerating expansion – you could claim that it’s a period of constant expansion, at least for a simple model, since H(t) stays constant through that period. The universe doubles in size on a fixed timescale throughout (an equivalent argument for the late-time dark energy dominated era is made by Sean Carroll in this post).

It’s also the case that if you’re in a universe going through some standard (radiation or matter-dominated) slow-down of expansion and an inflaton field switches on, then your expansion rate is unexpectedly higher than you would have na├»vely been expecting, but Andrew would argue that you’re doing things from ‘the wrong end’ if you do that:

(and playing with his interactive graphs on his explanatory page will invoke further commentary if you match to periods in or before inflation). I’m quite happy to do that in a discussion with a cosmologist, and I understand why we would do that, but I’m not sure most people think ‘backwards’ like we are prone to do.

If we don’t do that, and start from some pre-inflationary epoch in our discussion then it’s true that the comparison is not a particularly fair one, but I think it’s a more natural way to think about things, especially for non-cosmologists. We may not end up with a universe that matches the one we live in now if we consider a universe that matches up with ours at a pre-inflation time, and then don’t allow it an inflationary epoch, but I’d argue it is then ok to say that inflation is a period of fast expansion (it maintains a particular expansion rate from early times for longer), and use that as a starting point to discuss why inflation is important to actually get to a universe like ours. After all, if we start talking about it as a particularly slow expansion, how much more time do we have to spend explaining how it gets things out of causal contact?

One thing I’m definitely convinced of is that Javascript-y interactive graphs are a great explanatory tool!

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