Is the universe finite or infinite?

Ken G

Either one. Just not textbooks expressly designed to investigate speculative areas of astronomy. Such books always appear at the fringes of any science, they are certainly not quackery, but they are usually forgetten in a few decades-- such is the nature of controversial speculation. No doubt there are graduate textbooks on MOND, on loop quantum gravity, and on microscopic black holes.Good luck with that, I'm sure they'll be thrilled to have your expertise weighing in.
They told you that eternal inflation is a mainstream consensus idea? I doubt that strongly.
I don't see any quotes from them in your argument. What are you claiming they said, and why don't you think it is making it to the WMAP website?

twofish-quant

It would help if you gave me some authors.

Not really. MOND and LQC are changing too quickly for there to be much in the way of textbooks, so you end up with review papers and paper collections. Microscopic black holes are very interested from a theory standpoint, but there isn't much to say about them.

Well yes.

No they told me that

1) inflation doesn't require zero curvature
2) the current model of cosmology doesn't assume flatness

Give me a few days. If I can get you a personal email from one of the three people confirming my points, will you concede the argument? Also, I want to define the question, because I don't want to get into a situation where I bug someone who is busy, get an e-mail, and then you argue that the e-mail doesn't refute your point.

Conversely if you concede those two points now, you save me the effort of writing an e-mail.

1) inflation doesn't require zero curvature
2) the current model of cosmology doesn't assume flatness

Because the WMAP website was intended for non-technical people, and they simplify a lot of stuff in ways that could be misleading. That's why I'd prefer a reference to something stronger. If you have a citation to a paper in ApJ or a graduate textbook that argues that inflation is inconsistent with non-zero curvature, that would be different than a public affairs website.

Ken G

Obviously, it is very important to detail the issue correctly. The way you have paraphrased my arguments makes me doubt your version would have much resemblance. For one thing, you insist that I'm claiming that inflation implies the universe is flat. Of course it does no such thing, inflation is a model, it does not constrain the universe, rather the universe, in concert with the goals and demonstrable benefits of science, constrains the model. What I'm actually saying is threefold:

1) For inflation to continue to be regarded as a good model of what really happened in our universe, with no need for anthropic thinking, then curvature must never be detected, and conversely, if curvature is detected, then inflationary models will be up to their ears in anthropic justifications, so much so that much of their original purpose (to escape anthropic thinking) will be lost.

2) The current best model of the universe is a flat, infinite model that obeys the cosmological principle. Occam's razor contributes significantly to making this our best model. Its success is by no means a claim that the universe is actually flat or infinite, for indeed no model can ever make such a claim, given that we cannot see far enough to check it, and never will.

3) The question "is the universe infinite" could never be answered "yes" by any scientific means imaginable. It could only be answered "no", and we already know it cannot be so answered, because we already know we cannot see the limit of the universe. Even if we detect some tiny positive curvature, it would only mean that our best model was now a closed finite model, and again by Occam's razor-- not by any testable claim on the actual geometry of the universe that we cannot see. The best model is never a claim on things that observations are moot about, such things are adopted in the model purely based on Occam's razor. We must stop pretending that science can determine truths even after we have discovered that the observations cannot.

These are the three points I have repeated over and over, and I have never said, or thought, anything else of importance to this discussion. Anyone whose opinion you'd like to solicit on those three points would be more than welcome, indeed quite informative. But the way you have characterized my points is completely inaccurate, and framing the issue as you put it above would have no value whatsoever.

twofish-quant

And I strongly disagree. If it turns out that there is curvature that imposes a natural scale to the inflation. At that point we can look at the details of the inflation mechanism to see what physics would cause inflation to stop that that scale. For example, if inflation stops when some energy level reaches Planck's constant, then whatever stops inflation could be some quantum tunneling effect.

In physics this is called "hand waving" but it's a useful technique.

Again this is incorrect. Cosmologists do not assume that the universe is flat.

I'd argue that it doesn't. Where we don't add a term, there are reasons why a term is avoided. Occam's razor tends to be overused as a justification, and it's not that really useful in complex systems.

I think that you are limiting yourself. I *might* agree to the statement, if you put "currently imaginable" in that statement. Also, the statement of "assuming the universe is isotropic, must it also be infinite?" is something that *can* be answered yes or no.

But this is "proof by lack of imagination." Unknown is not unknowable, and if you want to convince me that something is "unknownable" then you have to give some quasi-mathematical proof of it. Then you run into the issue of whether something is unknowable is itself unknowable.

twofish-quant

Also just to clarify. Is assertion 1) something you got from someone else or something you made up. It makes a difference between if it's something you got from someone else, then it's easier if you just put a link to where ever you got the idea.

Also one other point is that neither 1) or 2) is "mainstream cosmology."

marcus

Ken I like some of your posts on other threads e.g. the multiverse issue. thoughtful and cogent. In this case your point #3 is extremely well taken. We don't expect scientists to claim X is the absolute truth. We are happy if they offer the simplest best fit model that has been devised so far and the most reliable model so far for predicting future observations.

So, as you say in point #3 if some positive curvature is discovered (with 95% certainty say) then the simplest best fit model becomes spatially finite. But like any scientific finding that would be provisional and no one can predict the future discoveries. The model might be revised down the road a ways.

That said, you might want to relax your points #1 and #2. I've always understood inflation as having leveled things out enough to be consistent with what we see today. Inflation is consistent with some slight residual curvature.

The treatment of inflation in Loop cosmology does not require fine-tuning and makes an adequate inflation era highly probable. It is consistent with some curvature and if curvature were detected would not bring on the "anthropery" bogeyman. Whether you get threatened by anthopery is to some extent model dependent. Some recent Ashtekar papers about inflation. So point #1 is not terribly firm.

Point #2 is a rather one-sided invocation of Occam, I think. Some people would put Occam on the side of a spatially finite universe, other things equal. I find the finite volume case easier to imagine, simpler. The infinite case with its infinite amount of matter and energy is quite a stretch to imagine. Uniformly distributed too! Infinite energy homogeneously distributed throughout infinite volume!

What you think Occam tells you is to some extent a matter of taste and community consensus. One doesn't want to be too dogmatic about what Occam says is "best". I think anyway.

There's a lot of good in what you say, here and elsewhere, but I think you might relax slightly on points 1 and 2 here.

Ken G

Here's the problem. You have an inflation model, and it has some parameter in it, perhaps the shape of some scalar potential function. You then look at the curvature today, run your GR backward until inflation ends, and try to match up what you get. Certainly you can take any current curvature, no matter how close to flat it is, and you'll get an answer to this exercise. The issue is what is the "size of the target" you are trying to match. If current curvature is not detectable at the, say, .0001 level, then you have a vast range of possible curvatures at the end of inflation, you just map from .0001, to 0, all the way back, and what you get is a hugely wide range of possible curvatures at the end of inflation. Now you have some hope that a plausible inflation model, that is consistent with other established physics, will "hit the target."

Now imagine some observation was just done that detects spatial curvature, say it's in the range .0001 to .0002. Play the same game, map that backward to the end of inflation, and now you have only a factor of 2 in parameter space-- that's the size of the target you have to "hit" with your inflation model. twofish-quant is saying that he has the hope that a plausible inflation scenario that is based on some atomic scale will rather magically hit this target. I'm saying that's pure hope, but at least it's a plausible hope if you have orders of magnitude of possible curvatures that fit with the modern observations. But let's say that a miracle occurs and a natural-sounding inflation model with some built-in established subatomic scale hits the target with finite curvature today. That will certainly seem like a convincing case for that inflation model, a slam dunk even.

But look at the cost we've had to pay-- first of all, we seem to have gotten really lucky to have hit the target, but that's what we are using to justify faith in our model. What's worse is, we now have to wonder why that subatomic scale happens to be set just to hit that tiny range, out of all the orders of magnitude of possiblities for a subatomic scale, so as to just barely generate measurable curvature today! The inflation model seems correct, even undeniable, but it's lost its main purpose: to be able to see the universe as not special or finely tuned. We'd be right back to anthropic reasoning-- the subatomic scale must be coming out that way so as to create a universe with small but measurable curvature because we couldn't exist in all the other more generic universes where that was not the case.
But I think it would. Look at it this way. Take the model you have in mind, and partition its possible parameters into two sets-- the set that leads to unobservable curvature, and the set that leads to small but observable curvature. Of course throw out the set that we've already falsified because it leads to huge curvature. Really do this, it should be easy enough with whatever model you have in mind. Now ask a simple question-- what is the relative measure of those two sets? Is it not true that the unobservable curvature parameter set has vastly larger measure than the observable curvature set? So how is it not fine tuned if we detect curvature tomorrow? How do you answer the question: why that parameter set and not the other parameter set, if the other one was orders of magnitude larger?
It is certainly true that Occam's razor is never clear-cut, but if you just look purely at the model, with no extraneous baggage that says the model is supposed to be the actual reality, then it is clear enough that a model with a non-arbitrary value for the flatness (i.e., flat) is simpler than one with an arbitrarily chosen value of curvature (how do you even give a value to it?). Also, it is much easier to use for doing calculations, which is the key issue I would say.Simplicity of imagining is a different flavor of Occam's razor, it's hard to say if a "best model" is the one that has the fewest arbitrarily chosen parameters (like flat versus some essentially randomly chosen curvature that is not refuted by observation), or the one that is "easiest to picture." My point is that once you are on board with point #3, you are relieved of any philosophical issues with an infinite universe, because you are not claiming the universe is infinite-- you are just fitting what we see to a flat model, like fitting a tangent plane to a manifold where you cannot measure any deviation between the two. The tangent plane is mathematically non-arbitrary, but it is hard to picture because it goes off to infinity in all directions. If we saw that as a bad thing, we could certainly do all of calculus to any precision with circles and spheres of small enough curvature, but we don't, we have lines and planes, because they are mathematically simpler, though harder to picture.

Ken G

Neither. It comes from me, but it stems from a logical argument. I summarized that argument again just above. So if you want to critique it, you do better finding an actual flaw in the logic.

You don't seem to even understand what I'm saying with 1) or 2), so I'm suspicious of your judgements of these points. For example, you insist on claiming that I have said that cosmologists assume the universe is flat. That is so completely different from anything I've said, or even thought, that I have no idea where you are even getting that from, but you can't be reading very carefully.

twofish-quant

If the curvature is positive then at some point in the life of the universe it will take all values from 1e-16 to infinity. We happen to catch it at 0.001, but wait a few billion years and it will be 0.002. Then 0.3, then 0.5, then 2, then 1000, then at some point dark energy takes over and it goes down again.


If there is *any* curvature, no matter how small, then the universe at some point in it's life will take all values between that small curvature and infinity.

No we don't. It's not a matter of hitting a target. As long as the inflation ends with *any* positive curvature, then things will work. It doesn't matter whether the minimum curvature is 10^-32, 10^-50, or 10^-100. Once the universe starts expanding from *any* small curvature, it will take *all* values between that small number and some limit at which when dark energy takes over.

So it doesn't *matter* what the minimum curvature is. It could be *any* number below observation. If it is 10^-100, it will eventually blow up to be 0.001. If it is 10^-32, it will eventually blow up to be 0.001. The only "magic" is that we see it at 0.001 rather than 0.002 or 0.01 which is what we will see if we wait a few billion years.

You are making quasi-anthropic arguments which I dislike. And no. It doesn't work that way. Suppose you end inflation with a undetectable positive curvature. This positive curvature will take all values from 10^-whatever and some large number at which you have dark energy take over.

Instead of taking multiple universes, lets just take one.

Now lets take a random point in the life of a universe with a positive curvature.

You have inflation and it reduces the curvature to some random small number. Now lets evolve the universe. It turns out that for most of the life of the universe, you will have a detectable curvature. If inflation ends with *any* positive curvature no matter how small, then at some point in the life of the universe, that curvature will take every positive value. So someone at some point will wonder why they observe 0.001, someone else will wonder why they observe 0.3, someone else will wonder they observe 1.0, and there is nothing to explain. You observe X, because you happen to be at the stage of the universe where you see X.

Philosophy would be easy if we didn't have to worry about observations.

twofish-quant

If it comes from someone else, then it's likely that it's already been critiqued and I can pop up google and replay the conversation.

You are saying that the best model used by cosmologists assumes a flat universe, and I'm saying that's not the case.

Communication is difficult, and if you aren't making that assertion, then what assertion you are making. You have said that LCDM assumes a flat universe, and that's false.

Ken G

But that's just it, the dark energy has already taken over. So we are pretty much at the curvature "peak" right now. That's the problem with a peak curvature that just happens to be what we can barely measure, why on earth would life come along at just the time when it can barely measure the curvature? That's the "fine tuning problem" that you would be staring at if curvature is detected, and that's what would steal most of the wind from inflation's sails.
No, not with dark energy.

Exactly, and if curvature is detected, then we will have the fine tuning problem that dark energy is taking over at exactly the point when the curvature is barely detectable by intelligent life. That's just the fine tuning that Weinberg argued is evidence for a multiverse, in relation to the amount of dark energy-- you would be in the exact same boat, but now in regard to curvature instead. You would need an anthropic argument to escape the appearance of fine tuning, and it would have to magically be consistent with the same anthropic argument that is supposed to be what lets dark energy be 10¹⁰⁰ time weaker than it "ought to" be. If we reject this is an escape hatch for the inflation theory, then we have no explanation for why the universe has a sense of humor that it will just let us glimpse the curvature before dark energy washes it away.
I agree completely, I don't think resorting to multiple universes is a fair way to make a theory seem palatable or plausible. That's exactly why I claim any inflation proponent should be hoping we never detect curvature, and indeed, should probably even be confident we never will. There's just no reason for the parameters of a working inflationary model to be so well perched at that arbitrary tipping point that would suddenly seem very special indeed.

I don't agree, I think that for the vast majority of ways to set up that universe, the curvature will remain way too small to detect, because the one-two punch of inflation and dark energy will insure that. That holds whether you imagine a cosmological constant or a quintessence-type continuous inflation. You have to really fine tune the combination of inflation and dark energy to both have a universe that inflates enough to be anything like what we see (and, dare I say it, to support life), but still leave a window for detectable curvature for a few billion years out of that vastly aging universe-- exactly when life comes along. That's the problem I've been talking about, this bizarre "glimpse of curvature" phenomenon, which has no "natural" explanation at all, and would sorely tax the whole spirit of using inflation to recover a "natural" feel.

Ken G

No, a thousand times no. Not only did I never say that, I bent over backward many times over to stress that is exactly not what I am saying. Yes, communication is the hardest thing, so let me repeat again what I have been saying. Cosmologists make models, and they make the models only as complicated as necessary to fit the data. The current models that do that are flat, and use the cosmological principle, so they are infinite models, like a derivative is an infinite model of a function even if the function becomes uncertain outside of some compact region. As I've repeated many times now, no such flat and infinite model can say anything at all about the infiniteness of the universe, indeed I stressed several times (there are at least three threads we are debating, so it's hard to keep track of where!) that the question "is the universe infinite" is fundamentally a question that science could never answer in the positive. But science can certainly, and does, make infinite models, if it has no evidence for making them finite. No such model is a claim on what we cannot observe, nor would there ever be any scientific validity in making any claims on such a region.Never said anything like that, nope. I said LCDM is a flat model, which is a totally different claim. It just says the simplest model that fits what we see is a flat infinite universe model, that is not at all "assuming the universe is flat." We don't make assumptions about the universe, we embed assumptions into models, in order to make good models, not in order to use models to make claims on the universe. The logic goes the other way-- observations of the universe inform our models, our models do not inform the universe that is outside the observations we used to make the model.

marcus

Things are getting clearer. You are not saying that mainstream cosmologists believe the universe is spatially flat, or infinite.

You are claiming that the predominant model in use, the LCDM, comes in only one version and that version is spatially infinite with zero curvature.

If you have never seen a cosmologist use a version of LCDM which has overall slightly positive curvature, then this claim is certainly understandable! It would square with your experience for you to insist that there is only the one version in use, with infinite space and matter.

However my experience is different from yours. I have seen top level cosmologists use different versions of LCDM, and for example, calculate a lower bound for the radius of curvature for the spatially finite positive curved version of LCDM.

You might recall this from the WMAP5 report by Komatsu et al (2010)

In other words, in my experience cosmologists do not jump to premature conclusions, do not gloss over different cases, and instead take the Omega confidence interval very seriously. Since the confidence interval has a substantial range above 1 that necessarily requires a spatial finite (but "nearly" flat) version of LCDM.

I think (if I understand you) we are getting closer to agreement because you are saying that cosmologists do not assume the U is spatially flat and infinite. I agree with you there.
If I understand correctly, you are merely saying that the LCDM model they use (but of course don't assume to be right) has only one version, which is exactly flat and infinite, spatially. And I disagree that there is only one sole model, not a confidence interval of different cases to which the model can be applied.

ViewsofMars

and
Brief comment, twofish-quant, the WMAP website is also used by the Smoot Group - Astrophysics and Cosmology. Might be worth reviewing their website:http://aether.lbl.gov/education.html

Dr. Smoot is also the Director of the Berkeley Center for Cosmological Physics and a winner of a Nobel Prize. I hope that helps with the ongoing discussion.

I have to go digging in my archives for further information I've stored to present to the discussions you are having with Ken on this topic and a few other topics.

Ken G

Right, most likely they believe almost as many different things as their are cosmologists, and indeed they are welcome to hold any personal beliefs they wish, but believing it wouldn't make it science.
There are always many multiple models in use, for a host of reasons, largely around the "buckshot" principle of doing science. But there is also a clear consensus on what is currently regarded as the best model, the model that is often heard in a sentence with "precision cosmology", and it is a model with no reason to include any curvature, so it doesn't. There's always the interplay between consensus and contrariness in science, and nowhere did I ever say that there is only one cosmological model that ever gets looked at-- I said there is one widely regarded best model, and Nobel prizes have been awarded.

Actually I have seen curved models invoked many times, my point is that none of those models ever gave us the value, the bang for the buck, that the flat model does. Indeed those models can now be seen to be largely a source of unnecessary complication. Almost all cosmology textbooks, for example, start out with the three possible geometries, and go to great lengths describing their differences, only to throw it all away when they come to describing the currently favored model! It's so much wasted overhead. I've no doubt that electromagnetism textbooks after Maxwell went to great lengths describing all the different ways light might operate in different frames if the speed of light was relative to an aether frame, but at some point, they realized that all that overhead was missing a key simplification that drastically simplified the mathematics of doing calculations-- Einstein's postulate. I'm saying flat models in cosmology are another example of just such a drastically beneficial mathematical simplification, to the point that it is becoming more and more apparent that we should embrace that simplification instead of fighting it every step of the way.Certainly. And many experiments in the era of Michelson-Morely were aimed at placing an upper bound on how much the speed of light could deviate from c in various frames. But at some point, the mathematical simplicity of a basic unifying postulate overwhelms all that careful overhead, and you just embrace what has been jumping up and down waving its arms at you all the while.
Just as in pre-Einstein days, they took the confidence interval on c very seriously too. And what is the confidence interval on c today? It's not infinitely narrow, right? So does that require we have a "very nearly relativistic" version of physics that we also have to bear in mind, and put in every textbook on relativity theory? Models are intended to be simplifications, there's no "conclusions" that are drawn when we adopt one, certainly not that we are announcing that we are convinced the model should suddenly be regarded as "correct," ignoring the fate of all "correct models" for time immemorial. All it means, when we adopt a particular idealization in some model, is that we are tired of doing extraneous and unnecessary work tracking what is much simpler to just remove from the model. We have simply reached the point of diminishing returns for tracking the complexity, relative to just adopting the simpler postulate. I'm saying cosmology is at that point, but it might take it a little while to make the transition.

Edit: let me rephrase that, I'm not trying to tell cosmologists how to do their business, I'm pointing out that we may very well be approaching a time when we need to give very serious consideration to treating the flatness of our models as a physical principle. Note this still does not represent a claim that the universe is actually flat, any more than relativity is a claim that the photon is exactly massless, it is merely a recognition of the value in adopting a particular mathematical simplification in our best models. That is also an accurate description of the theory of relativity, despite how it is often framed in less scientifically careful terms!

ViewsofMars

Picking up where I left off.

Nature 404, 955-959 (27 April 2000) article:

marcus

Ah. This is where your personal attitude comes in. I remember in another thread you were urging that students not be exposed to the spatially curved versions of the model. You are campaigning for a kind of educational reform, in effect. Cosmology textbooks and curriculum should not WASTE STUDENT'S TIME by introducing the slightly curved case, or cases. It is "unnecessary complication"

The course outline, in effect, should focus exclusively on the flat case.

But not because flat is BELIEVED by any kind of mainstream majority or consensus.

Indeed to illustrate, in a central paper like the 2010 WMAP5 report by Komatsu et al they were keeping their options open and calculated up front with THREE versions of LCDM showing their results already on page 3 as I recall, Table 2, I think. A central paper with a dozen big name cosmologists reporting on a flagship project. Not fringe.

You are advocating a curriculum reform, to save "overhead", which would render students incapable of undertanding the options being kept open by core top professionals in the field.

It strikes me as a bit short sighted, a false "economy". It seems to have no logical basis, since we do not KNOW curvature is zero, and we may in future discover that it is on the positive or negative side of today's rather broad 95% confidence interval.

There is no logical basis for you to insist on this change in the course outline. It seems to have more to do with PERSONAL AESTHETIC.

I guess if we are going to talk at the level of personal aesthetics, prejudices etc. I will state my own, about what beginning cosmology students should be taught.

I would wish the course to present and explain the current confidence interval for Ω_k from the WMAP7 report (also Komatsu et al) and, assuming today's best estimate for the cosmological constant, describe the two basic kinds of universe contained in that confidence interval, both indefinitely expanding, one with slight positive curvature and the other with zero or slight negative. One model spatially finite (now and at the start of expansion) and the other infinite (now and at the start) or topologically rather intricate.

I'll go get that confidence interval for Ω_k Just google "komatsu wmap 7" and you get
http://arxiv.org/abs/1001.4538 and page 3 says:
−0.0133 < Ω_k < 0.0084

which means:
0.9916 < Ω < 1.0133