Does Spatial Curvature Falsify Eternal Inflation?

[windy miller]

I have often heard it said that the picture of a multiverse inspired from eternal inflation is not falsifiable. However this paper from 2012 claims that it is:
https://arxiv.org/pdf/1202.5037.pdfspecifically it says, as I understand it, that if one were to measure sufficient positive spatial curvature this would falsify eternal inflation.

So what is going on here? Do the people that make these claims not know of this paper , or is there a known flaw in the papers claims? or...? Any guidance much appreciated.

 

[PeterDonis]

Moderator's note: Thread title edited to put in the form of a question.

@windy miller if you're asking a question, not making a claim, your thread title should not read like you are making a claim.

 

[windy miller]

Thanks , It's the title of the paper and I am asking about the paper, but I see your point.

 

[PAllen]

It certainly seems people in the field are well aware of this paper. It has 50 citations so far. I haven't looked at any of them, just thought it worth pointing out.

 

[kimbyd]

I have often heard it said that the picture of a multiverse inspired from eternal inflation is not falsifiable. However this paper from 2012 claims that it is:
https://arxiv.org/pdf/1202.5037.pdfspecifically it says, as I understand it, that if one were to measure sufficient positive spatial curvature this would falsify eternal inflation.

So what is going on here? Do the people that make these claims not know of this paper , or is there a known flaw in the papers claims? or...? Any guidance much appreciated.

Skimming the paper, it seems quite reasonable to me. However, I doubt that finding curvature in this narrow band in future observations will necessarily be significant evidence for eternal inflation. It's good to know that there are possible future observations which will rule eternal inflation out, but it'd be nicer if it was a prediction that couldn't be explained by a great many other models.

This gets a bit into the philosophy of science, but generally I think the focus on falsifiability is too narrow. Falsifiability is important, but it's often just as important for there to be distinguishing characteristics that really set the theory apart from others in observable ways. For example, a positive detection of primordial gravitational waves would be a strong signal that really sets some early-universe theories apart from others. A lack of detection doesn't do the same thing: most theories have a range of parameter space where the gravitational waves are either absent or too small to ever be detected.

Alternatively, some years ago there was a model proposed that requires significant positive spatial curvature:
https://arxiv.org/abs/1104.3315
Finding curvature within the bounds predicted by this model would have been much more interesting, because it's predicting a value that most models do not. Other models may fit the value, but it would be a surprise that they would just accidentally land on a curvature value that fits within this model's prediction.

So I think this is a useful result, and will be interested to see what future spatial curvature measurements turn up, but I'm a little irked by the side issue of falsifiability the paper brings up. It's also important to recognize how surprising the result is given various models. With curvature measurements, it's possible in the future that eternal inflation will be falsified. But it's not possible to really increase our confidence in eternal inflation with any curvature measurements.

 

[kimbyd]

Also, a side comment on the correctness of the paper:

The overall result of the paper is probably completely accurate. Measuring curvature is likely to rule out eternal inflation in part or in whole. This is a result that has been arrived at by other theorists as well, but the details differ.

What I have less confidence on is the precise numbers. But to me that question is less important at the moment, as we don't have measurements this accurate yet. When we do have measurements this accurate, then it will be important for many other theorists to take a really close look at this and similar results and make sure they're accurate in detail, not just in the overall picture.

Note that there is also the possibility that some theorists will find clever ways to force eternal inflation to allow some significant spatial curvature. Sometimes theories like that are reasonable, but often they're pretty obviously contrived. We'll see if we get there. There are quite a few theorists working in this space, and so I expect a lot of activity if we get curvature measurements this precise.

 

[windy miller]

Also, a side comment on the correctness of the paper:

The overall result of the paper is probably completely accurate. Measuring curvature is likely to rule out eternal inflation in part or in whole. This is a result that has been arrived at by other theorists as well, but the details differ.

What I have less confidence on is the precise numbers. But to me that question is less important at the moment, as we don't have measurements this accurate yet. When we do have measurements this accurate, then it will be important for many other theorists to take a really close look at this and similar results and make sure they're accurate in detail, not just in the overall picture.

Note that there is also the possibility that some theorists will find clever ways to force eternal inflation to allow some significant spatial curvature. Sometimes theories like that are reasonable, but often they're pretty obviously contrived. We'll see if we get there. There are quite a few theorists working in this space, and so I expect a lot of activity if we get curvature measurements this precise.

Thanks for this. I also agree that falsification is over rated. I think its a desirable property of a theory, but not the be all and end all. A lot fo the debate about the multiverse often is framed as a debate about falsifiability. With advocates appearing to deny its importance and critics claiming its the deciding issue for demarcation between science and non science. However if eternal inflation is actually falsifiable then the issue of whether falsifiability is needed for science becomes a red herring in this case and that is something that I think is largely under appreciated.

Another question for you , if you don't mind, what sort of experiments can improve the curvature measures over the next few decades?

 

[kimbyd]

Another question for you , if you don't mind, what sort of experiments can improve the curvature measures over the next few decades?

Improving curvature estimates is mostly an issue of better galaxy surveys. The CMB data itself is accurate enough on this point that we won't gain much on that front for curvature estimates. Galaxy surveys can add a lot here, from a variety of directions. Baryon Acoustic Oscillations are a big part of this: these use large-scale galaxy surveys to estimate the two-point correlation function between galaxies. The two-point correlation function describes the typical separation between galaxies, and has a characteristic bump at a specific distance caused by the plasma physics in the early universe. The distance for this bump is related to the distance scale we can see on the CMB sky, and thus allows us to observationally compare lengths between the early universe and the later universe.

By observing many more galaxies, the constraints on curvature can be made much tighter. This involves a mixture of new satellites (e.g. JWST), larger telescopes (e.g. TMT), and simply spending more satellite time observing the sky.

 

[windy miller]

Improving curvature estimates is mostly an issue of better galaxy surveys. The CMB data itself is accurate enough on this point that we won't gain much on that front for curvature estimates. Galaxy surveys can add a lot here, from a variety of directions. Baryon Acoustic Oscillations are a big part of this: these use large-scale galaxy surveys to estimate the two-point correlation function between galaxies. The two-point correlation function describes the typical separation between galaxies, and has a characteristic bump at a specific distance caused by the plasma physics in the early universe. The distance for this bump is related to the distance scale we can see on the CMB sky, and thus allows us to observationally compare lengths between the early universe and the later universe.

By observing many more galaxies, the constraints on curvature can be made much tighter. This involves a mixture of new satellites (e.g. JWST), larger telescopes (e.g. TMT), and simply spending more satellite time observing the sky.

thanks, that is really interesting .Ii really appreciate you taking the time to answer.