Alan Guth on the significance of the horizon and the flatness problem.

Guth:

Actually, it really did take a while before I regarded the horizon problem as being as significant as the flatness problem. Now I think I regard the two as being equally significant.

Lightman:

Why was that? Why did you regard it initially to be less significant than the flatness problem?

Guth:

I think the reason I certainly would have given at the time was that it’s a problem whose statement is less quantitative. With the flatness problem, you have this number, the expansion rate at, say, one second, which has to be tuned to 14 decimal places. If you want to phrase it at grand unified theory times it’s even more — 49 decimal places. The horizon problem is always just qualitative — you don’t understand why the universe looks the same here as it does there — and for that reason it impressed me somewhat less.

Lightman:

Because what you mean by uniformity of temperature is hard to quantify. You can certainly state quantitatively what is the largest angular size over which things were in the horizon at a z of 1000, when the microwave radiation was produced. You can certainly state that quantitatively.

Guth:

Yes, that’s right. But I guess I was less impressed because there’s no colossal number that you have to explain. The horizon is not that small. The causal horizon is maybe a factor of 100 smaller than what you’d need to cover the entire observable universe, but not a factor of 10¹⁵ or 10²⁹. I suspected that there was enough ambiguity so you could find some minor way of changing the physics of the early universe, without something dramatic that might very well get around the horizon problem.

Lightman:

I see. But you say that since you’ve been thinking about it more, that you have come to elevate its importance to that of the flatness problem?

Guth:

Yes, I think so. Why? [pause] Well, certainly the strongest influence is probably just the psychological importance of time. In the end, of course, it’s not really a scientific question to ask which of these problems is more important. It doesn’t affect anything that you’ve concluded about what’s true or false. Emotionally, I regard the two as on equal footing. In terms of the role they play, I think the role of the horizon problem has enlarged somewhat. It enlarges when you consider a question that came up after inflation was proposed. The people who were strongly convinced that omega was really 0.2 rather than 1, some of those people advocated the idea of limited inflation — inflation that would cut off at just the right point so that omega doesn’t get driven to one. I think the strongest argument against that is basically the horizon problem of sorts, that is, the uniformity of the cosmic microwave background. If you have inflation which cuts off before it drives omega to one, it means that you're still leaving significant influences from the initial conditions, before inflation, in the observable universe.