# Don't even know which question to ask first

1. Jan 27, 2010

### GreatBigBore

I've been trying to understand some basic stuff about cosmology for years, and I still can't quite get there. I'm not even sure which part of it I'm misunderstanding, and don't know what questions to ask, so I'll just start blasting out the questions and see if anyone can help me make sense out of it.

So, first question has to do with geometry and topology I think, but I'm not sure how. Let's say that I can stop time completely right now, and I travel four billion light years in a straight line, in any direction (please, don't confuse me by asking me what I mean by "straight line"). Can anyone help me to understand what significant differences I'd see in the sky? Obviously different stars, but what I'm trying to get a handle on is this idea that nowhere is the center, but the universe isn't infinite. I understand the "open/flat/closed" geometry issue, or at least I think I do. I've heard our closed, finite space made analogous to the surface of a sphere. But I've also heard cosmologists assert that our universe is as flat as we can measure, so the sphere analogy doesn't work, I think. It seems to me that if I went four billion light years in some direction, I'd perceive that I'm getting close to the "edge" of something, that I'd see less in some direction: fewer galaxies? Ok, that's enough of a dumb question for now. If I can make sense out of that one, maybe I'll know what question to ask next.

Twofish-quant, feel free to wait on answering until everyone else has weighed in. When I read your responses before everyone else's, my head explodes, and then there's a mess, and my mom gets mad.

2. Jan 28, 2010

### Chalnoth

Everything would remain more or less the same. I mean, yes, there would be different stars, and different galaxies. But any sort of statistic that describes the visible universe as a whole would remain unchanged (to within some small random variance). For instance, the average matter density would be the same, the average dark matter density would be the same, the average dark energy density would be the same, the typical separation between galaxies would be the same, the CMB temperature would be the same, the distance to the CMB would remain the same, etc.

This is known as the cosmological principle: the universe is (on average) the same everywhere and in all directions. For a long time the cosmological principle was merely assumed, not because there was really any compelling reason to do so, but rather because it was the easiest thing to consider. But as more and more experimental data has come in, every observation has held up the cosmological principle as being valid, at least for a ways out (I don't think anybody expects it to be valid for infinite distances, but it definitely appears to be valid for some distance beyond what we can see).

In the flat case, you'd just pick a different topology, such as a torus. The same principle applies though.

In any case, we don't necessarily know how big our universe actually is, or whether or not it wraps back on itself. Even if we detected that it was locally closed or open, we still couldn't say whether or not it wraps back on itself (because it certainly doesn't do so within our visible region, as we've looked for this). We just know that it is very, very big: much bigger than the small piece of it we can observe.

3. Jan 28, 2010

### GreatBigBore

Yeah, I've heard that answer before too, and I still don't get it. Maybe I need to ask the question differently. How about this: if I stop time and just start traveling in a straight line, will I ever arrive back at my starting point? And, if I stop time and travel in a straight line to the location where we currently see the last scattering surface, what would I see there? (In general, obviously. I know that I won't find Elvis.)

Umm, yikes. Maybe I need to go to the "for Dummies" forum. *Distance* to the CMB? I thought that the CMB is everywhere. I'm hoping that you mean the distance to the last scattering surface. But now that I think of it, I can't make sense of that either.

Unfortunately, from within my confusion, a torus looks the same as a sphere: the only relevant characteristic I can see is that the surface curves back on itself, just like that of a sphere.

4. Jan 28, 2010

### bapowell

Right, the torus does look like a sphere, that is, when it's embedded in a 3D space so that we humans can visualize it. But a torus is indeed flat (you can make one by identifying opposites sides of a flat rectangle.) However, the benefit of that pesky embedding is that it reveals that a torus is closed, just like a sphere, in the sense that if you walk far enough in a given direction, you'll eventually loop back on yourself.

Also, the CMB is everywhere. By "distance to the CMB" Chalnoth does mean distance to the last scattering surface. This surface does not have a physical location -- if you stop time and go out far enough you won't eventually run into it. This surface is best understood using the following setup:

Draw the earth at the center of giant sphere. This giant sphere is the last scattering surface. Each CMB photon that reaches earth today was on this sphere when the CMB was generated 14 billion years ago (ignoring incidental rescatterings and effects from reionization). If you stop time and move out across the universe, you remain at the center of this sphere!

Lastly, while the universe does appear to be rather flat, this measurement only describes our observable universe. Our observable universe could be a tiny patch on a giant sphere, in which case the observable universe would look to us the way the earth looks to us -- flat. But again, the topology of the universe really is key here, and the local geometry does not necessarily tell us anything about the global topology.

5. Jan 28, 2010

### GreatBigBore

Sounds like I don't really know what a torus is. Is it easy to explain to me how something can be flat and closed? Or will it just degenerate such that I'd be better off getting a book? Or maybe a URL that has a good primer on topology?

Yeah, I understand that the last scattering surface isn't an object. I just was trying to visualize what I would see if I could go to that location. I'm trying to educate my faulty intuition, which keeps telling me that if I went there, I'd see some indication in the sky that I'm nearer the edge of something, or back within view of Earth in front of me, or at least I'd see something that would be consistent with one or the other of those possibilities.

6. Jan 28, 2010

### Ich

That's quite easy, in one dimension: a cylinder surface has no intrinsic curvature, so it is flat in the GR sense.
It's more difficult with the torus, which isn't actually flat. You can't embed a 2D surface with no edges in 3D space while keeping it flat. So it's definitely not easy to explain or imagine, but mathematically rather simple, as you don't have to embed it in higher dimensions.
If the "edge" were much farther away, you would see no indication. Current consensus is that we'll see no change as far out as we can get information from. What's behind that boundary isn't important, we can't know anyway.
Maybe this is true. All we can say for sure is that we found no evidence for such a periodicity on scales of ~50 Gly.

7. Jan 28, 2010

### bapowell

Sorry, I shouldn't have said looks like a sphere. I meant looks curved like a sphere. A torus is a donut, as you know. Don't mean to confuse. The closed part comes from the topology, which for the sake of discussion, is just a set of rules for how to glue the edges of a rectangle together. The famous example is the old Atari game Asteroids -- it's a 2D world with rules that say "when you exit screen left, appear from screen right", and same for up and down. This is toroidal topology. You don't need a 3rd dimension (or curvature) to make a torus. It's the rules (topology) that close the surface. I don't know of any good primers.

I was trying to explain that the LSS is not a present-day location that you could go visit. It's the collection of points from which CMB photons reaching earth today were emitted 14 billion years ago.

8. Jan 28, 2010

### GreatBigBore

Oh boy. Sounds like I need to do some studying. I'm like, wait a second, spheres have curvature but cylinders don't? I'll bone up and come back!

Whoa, what do we use for testing such huge periodicity? Is it strictly theoretical or is there a physical basis for it? And that leads to another of my zillion questions: Krauss says that we know how many particles there are in the universe. I recall a calculus professor saying something about 10^85 as an estimate, but Krauss insisted that we *know*, and we use the knowledge to convince ourselves that dark matter isn't just ordinary, non-luminous matter. I would love to know how we reached a firm conclusion about the particle count (or it may have been proton count).

Ah, but this goes right to the heart of my compulsion to get my head around this and get involved in the discussion. I've had a religious experience recently. When I first heard Sagan say, all those years ago, that we are the cosmos recognizing itself (or something like that), I thought that he was a kook. But I suddenly get it: we *are* the mind of the universe! No, that doesn't put it in perspective. Nobody says, "I am the mind of this body." We just say, "I am me." (Ok, we don't say it, but it's implicit.) We *are* the universe.

Whoa.

Even if we're not entirely alone, consciousness has got to be pretty darned rare. We have to figure out how to get around these boundaries, to take control of the very fabric of things, so we can figure out what we are, who we are. I can't be the only one here who often finds himself sitting there considering everything we know and don't know about how we find ourselves here, and then, almost like waking up with a shock, look around and go, "What the hell?" We have to answer that question.

Maybe all our religious visions had a grain of truth to them: maybe the universe itself (you and I!), becoming conscious, gaining control over its body like a living thing, is a sort of god. We have to get out there, find our siblings (if there are any), and become something undreamable. We owe this to ourselves.

It's fun to be all cynical and say that the reason no aliens have visited us is that they're too smart. But think about it. What do you do when your kid brother is acting like an idiot and getting himself into serious trouble? You don't let him get himself killed. What that tells me is that we're the first to wake up, or among the first, or perhaps--and this gives me chills--the only ones. We've got to figure out a way not to blow ourselves up.

Anyway, I want to be part of this craziness, even if it can't even be dreamed of by engineers for another 500 years, or 5000. *sniff* I made myself cry.

9. Jan 28, 2010

### Chalnoth

1. We don't know, because we don't know the overall topology of the universe yet.
2. You'd see a different region whose properties are the exact same as ours. You see, the light that we see from the last scattering surface was emitted 13.7 billion years ago. The stuff that emitted that light has been doing stuff this entire time, and is now a region of the universe that, statistically, looks just like the stuff we see around us.

Yes, I do mean the distance to the last scattering surface, which is the distance to the stuff that emitted the photons that we are seeing today. Tomorrow, we'll be seeing photons that came from just a little bit further away. Next year we'll be seeing photons that came from just a little bit further away than that, and so on and so forth. So the distance to the surface of last scattering increases with time, not because it is physically increasing, but because we're seeing that part of it whose photons took a little bit longer to get to us.

Except that the curvature of a torus is flat. This may not be completely obvious, but basically a flat surface is any surface that you can make out of a flat piece of paper without stretching or tearing. For example, you can make a cylinder out of a flat piece of paper without any stretching. But you can't make a sphere.

A torus requires a little bit of explaining, because if you make a torus in three dimensions, it does require some stretching. On average, the curvature is still flat (there's some positive curvature on the outer bits, some negative curvature in the inner bits). But you can mathematically write down a torus that is perfectly flat. In fact, in four dimensions, you can even make a 3-dimensional torus that is perfectly flat.

One way of visualizing this mathematical construct is to just look at the game of asteroids: when you travel out one side of the screen, you appear at the other. This is toroidal topology: it's flat in every direction, and yet still wraps back on itself.

10. Jan 28, 2010

### George Jones

Staff Emeritus
Intrinsic curvature is a measure of how much geodesics deviate form each other. Take a sheet of graph paper and roll it up into a cylinder. The lines on the graph paper deviate no more from each other when the graph paper forms a cylinder than when the graph paper lies flat on a desk. The is true even for a set of parallel "inclined" lines drawn on the graph paper.

11. Jan 28, 2010

### Phyisab****

"That's quite easy, in one dimension: a cylinder surface has no intrinsic curvature, so it is flat in the GR sense."

lol I'm about to get a degree in physics and I was still like "wait, what?" This is the perfect way to confuse the crap out anyone without prior education in geometry.

12. Jan 28, 2010

### bapowell

It might be good for responders to read the posts given before them so as not repeat things.

13. Jan 28, 2010

### Ich

Yes, you can roll a sheet of paper without doing harm. That's called no intrinsic curvature, the kind of curvature some "flatlanders" could measure. It has "extrinsic" curvature, however, but that's irrelevant.
They're looking at http://arxiv.org/abs/astro-ph/0310233" [Broken].
Yeah, Krauss.
There's always one pitfall: when people are talking about "the universe" and it size, mass, particle number and so on, they usually mean the observable universe, but forget to mention that. We don't know how big the universe is, we don't know how many particles there are. We just can make an educated guess at how many particles there are in the part of the universe that we can know about today.
I can't speak for you, but I'm just a physicist.
Um, will half an universe and a physicist do also? Or just half an universe, me staying here, conscious most of the time anyway?

Last edited by a moderator: May 4, 2017
14. Jan 28, 2010

### Chalnoth

50Gly is approximately the current distance to the surface of last scattering.

15. Jan 28, 2010

### GreatBigBore

Ok, I can live with the caveat about observability. But still, how do we arrive at this guess, and what is the basis for our confidence that it rules out normal, non-luminous matter as dark matter?

I'm not sure what you mean, but given the loftiness of my speech, it's probably safe to assume that you're teasing me. You can stay here. I'll send pictures. Of me. Doing green chicks.

16. Jan 28, 2010

### GreatBigBore

One major *click* sound just happened in my head. Thanks! But of course, now more questions come up. Now I can possibly give a useful formulation to my first question: if I could stop time right now and travel in a straight line 25Gly minus 15 feet, what might I expect to see? Or might I even expect to be unable to travel that far because I'd bump into something before that? I'll just let it be believed that I think there's something to bump into, because I truly have no better alternative to imagine.

Twofish-quant, feel free to respond now, because my head just now did explode.

Last edited: Jan 28, 2010
17. Jan 28, 2010

### bapowell

The acoustic peaks in the spectral decomposition of the cosmic microwave background offer tons of information about the observable universe. They give the frequencies with which the plasma of the early universe was sloshing about. You can pinpoint the density of baryonic matter because baryons increase the effective mass of the plasma (think harmonic oscillator). The bottom line is that you can determine the baryon density by carefully measuring the amplitudes of the peaks of the CMB spectrum. The peaks also give information on the dark matter content of the universe.

Other data, like that from Large Scale Structure surveys, give additional evidence for nonbaryonic dark matter. Without dark matter, galaxies form later and it's difficult to get a universe that resembles ours. I can talk about that more if you're interested.

18. Jan 28, 2010

### Chalnoth

So yeah, this doesn't change things much. Obviously the further you go, the less confident we can be that the cosmological principle will hold, that everything you see will be the same (on average) as it is here. But the fact that our universe is so uniform out to the surface of last scattering (we only see deviations of one part in 100,000 on the CMB itself), we can be pretty confident that the cosmological principle holds for at least a factor of a few times the size of the bubble we can observe.

That said, let me point out that it may well hold for an absurdly larger region. Due to the exponential nature of its expansion, if inflation only lasted twice as long as required to explain the flatness and homogeneity of just the region we observe, then it would have generated a region that is 10^30 times larger on a side than the part we observe.

19. Jan 28, 2010

### GreatBigBore

Naturally I couldn't keep up with all of your details, but I understood enough of the broad concepts to be satisfied for the moment. But then I tripped on this last thing. We weren't talking about a no-dark-matter universe before, so I'm guessing that maybe there's a typo somewhere? Or that I'm missing your meaning, anyway. Did you mean that if dark matter were baryonic then galaxies would form later?

20. Jan 28, 2010

### Chalnoth

I'd just like to add a bit about intrinsic curvature, because I'm not sure it's been adequately explained yet.

As George Jones mentioned, intrinsic curvature is a measure of how much geodesics deviate from one another. But what does this mean?

First, what is a geodesic? For this, we have to go back to Euclid, and his definition of parallel lines. One of the perhaps perplexing things about Euclidean geometry is that Euclid never was able to prove that parallel lines never meet: he had to put that into his geometry as an axiom. This may seem a little strange. You'd think that it's something that could be proven rather easily, because it's just so obviously true.

But the problem is that it's not true. At least not all the time: it's only true for flat space. In order to prove that parallel lines never meet, you have to allow for the possibility of curved space. But then there's a problem: what is a straight line in curved space? After all, if space itself is curved, then aren't straight lines impossible? In a sense yes, this is true. However, you can generalize a straight line, and there are a few ways to do this.

One way to generalize a straight line is to take a particular property of straight lines in flat space: in flat space, a straight line is the shortest distance between two points. In curved space, the shortest distance between two points is called a geodesic. A geodesic also has the interesting feature that if, for example, you are sitting on the Earth and decide to move in one direction without deviating at all, you will end up walking along a geodesic. So this seems to be a very natural generalization of a straight line.

So when we are talking about geodesic deviation, we are going all the way back to Euclid and his axiom that parallel lines never meet: by measuring how far away parallel lines (geodesics) actually do meet (or get further from one another), we get a measure of how far we deviate from flat space.

To take a perhaps familiar example, take the Earth. A geodesic on the Earth is called a great circle: it's the circle you would make if you were able to walk in one direction without deviating. Some examples of great circles are the equator and lines of longitude (not lines of latitude besides the equator, however). If you take two different lines of longitude, for instance, these are perfectly parallel at the equator. But as you move towards the poles, they get closer and closer together. This is because the Earth is curved.

This definition of curvature is also why any shape you can make out of a flat piece of paper without stretching or tearing is a flat surface. Imagine drawing a grid on this flat piece of paper: any change you make to the paper that leaves the distances between grid points unchanged doesn't change the curvature. And only if you stretch or tear the paper do you change the distances between grid points.

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