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Universe's Curvature Measured?
jmobiusmaximus writes "Right next to the wormhole site on the BBC News page is an article about the results of the Boomerang project in Antarctica. This resulted in a new map of the 2.7K cosmic microwave background radiation, which is thought to be a remnant of the energy released in the Big Bang. The BBC News synopsis isn't bad, and has some links that will answer most "WTF?" questions. For those of you who have taken a little bit of physics, the original Nature article is better. This could have a large impact on our understanding of the universe's evolution and will probably be the source of much debate in the near future.
"
My Ideal universe:
- Has Flat Curvature
- Has Positive Curvature
- Has Negative Curvature
I'm all for Positive Curviture. Yeah, Baby!
Anomalous: inconsistent with or deviating from what is usual, normal, or expected
Anomalous: deviating from what is usual, normal, or expected
Canard: a false or unfounded repor
If I remember correctly the universe is supposedly saddle shaped... hence the curvature of the universe being a measurable thing...
What I've never understood is what is meant by that... does all the universe's matter (planets, stars, etc) fit into a saddle shape? If so, is there any particular reason why?
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The problem here is that they are talking about the curvature of four dimensional space time. One way for us to visualize this is to pare things down to a two dimensional sheet. Imagine teh universe is a plastic sheet lying on the floor. The sheet can be flat, having zero curvature (because the second derivative of the sheet "height" is zero), or it can be curved. If it has negative curvature everywhere, it could be something like a sphere. A saddle on the other hand has positive curvature. That is, the second derivative is positive somewhere.
All of this seems kinda wacky when applied to four dimensions. We can't visualize four dimensions easily, let alone what thier geometry looks like. And that is really the point here. On a flat surface (universe), normal Euclidean geometry holds. E.g., two parallel line never intersect, the sum of the interior angles of a triangle is 180, etc. On a curved surface (universe), this is not true. Draw a triangle on a deflated ballon (the flat universe) and then blow it up. The sum of the interior angles increases.
Pretty neat, huh? And that is some of the reasons they are looking into this.
This just leads to the more interesting question. Why is the universe flat? After all, the visible matter (stars, galaxies and nebulae) constitute only 1% of the required amount of mass to keep the universe flat. What is the condidate for the other dark matter? (We know that there must be lots of dark matter around from rates of rotations of galaxies). This is a very controversial topic and worth lots of man-hours of work in cosmology. Whatever the candidate is, it should also explain why the universe is so flat.
There I was, all intrigued to see whether the cosmological constant was about to bite the dust and finally lay Einstein's "greatest mistake" to rest, and all they've found is that the universe is flat within 12%. Oh well - have to wait for the next set of results. I'm still rooting for Omega_m to be 1 just so that the universe is old enough to hold its oldest constituents ;-)
Cheers,
Toby Haynes
Anything I post is strictly my own thoughts and doesn't necessarily have anything to do with the opinions of IBM.
I'd advise Slashdot readers to look at the Cosmology and Relativity FAQs, since they probably answer a lot of questions people are tempted to ask.
Does this mean that if one flies in a spaceship far enough, they can "fall" off the end of the universe?
Don't be silly. There's no gravity at the end of the universe. Didn't you see the sign?
Should we send a "Columbus" probe out to find out?
It's already been done. Columbus 1 was launched in 1978 as part of NASA's top secret "Top Secret" programme. It used a quantum tetryon drive to transport itself instantly to Zeta Reticuli, where it claimed the planet in the name of the Earth. It then spent the next twenty years slaughtering the native population and replacing it with Earthmen and women. The new population has a lot of wacky ideas that they're trying to foist on the rest of the universe, like the freedom to bear tactical nuclear weapons and a literal interpretation of Lord of the Rings.
This is confirmation at a universal scale of the matter/energy equivalence. i.e. the entire energy of the universe exactly is balanced by the force of gravity.
If this is true then:
There REALLY is missing "dark matter" at least 70 percent of the universe is unknown to us.
The "heat death" ( entropy increasing )of the Universe is going to be our/its final fate. ( Unless that dark matter has some exotic properties we don't know about, which at this point would not suprise me )
And apparently there is such thing as a "Free Lunch" ( as in beer ). We don't have to pay back the Big Bang with a Big Crunch.
I kinda was hoping for alternating Bangs and Crunches, it allows one to imagine perhaps existing again in another iteration.
A Universe that lasts forever and dies an entropy death kind of does not allow that.
How depressing...
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Since inflation theory (originally proposed by Linde in 1985 IIRC) predicts (well, demands might be a better term) that the cosmological constant be equal to zero, this is a victory for this theory, albeit one that practically everyone involved in cosmology expected a long time ago. But the question still remains, why is the Universe flat?
According to our current estimates of the density of matter in the Universe, the curvature of the Universe should be negative (producing a hyperbolic, "saddle"-like shape), producing a Universe where expansion continues forever and the Universe eventually dies from "heat death" as thermal equilibrium is acheived throughout the entire Universe.
But this measured value is out by a factor of 100 from the necessary value for the Universe to be flat (referred to as omega by cosmologists). Where is the missing 99% of the mass of the Universe? The point of this study is that the data is inconsistent with a lot of the more "exotic" models of this missing mass - topological defects, WIMPs and so on. But the data is consistent with the so-called "cold dark matter" models, which includes things like black holes which could be everywhere but are too dark for us to see.
Of course this is just one study, and the whole question is still open in a scientific sense. But this does provide some good evidence for inflationary theory as well as some additional data for cosmologists working on where the "missing mass" of the Universe is.
So is that why you rarely ever see the Enterprise fly over / dive under an enemy to evade fire? Cause they'll hit the edge? ;-)
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Let me chime in as a member of competing team (http://topweb.gsfc.nasa.gov) that did not make it on time to get all the credit.
This is the great result, comparable only to discovery of microwave background radiation in 1965 and first detection of CMBR anisotropy by COBE in 1992. It tells us much more then flatness of the Universe. From the results of this and followup experiments (ours will be somewhat more precise when we finally do it) it will be possible to find how much of the matter in the universe is barionic (composed of protons, neutrons and electrons) as opposed to stuff we have no idea about, which is probably contains up to 90-95% of the mass of the Universe. It will be possible to measure often mentioned energy of vacuum (do not count on using it --- not only it is low, it is also unextractable). Boomerang already a strong evidence in favor of inflation --- a strange theory, describing how most of matter in the universe was created from nothing, just because its positive rest energy was compensated by negative gravitational energy, so that total energy of the flat universe was and remains zero (this is how you create the whole Universe from nothing without violating the law of energy conservation). Future experiments will tell us more about how inflation happened and what kinds of fields and particles are responcible for it. We definetly will learn new things about fields and particles at energies far above what can be achieved in accelerators.
We live in interesting times.
BTW, read http://www.astro.ucla.edu/~wright/cosmolog.htm --- it is a good introduction to cosmology.
The problem here is that they are talking about the curvature of four dimensional space time.
Why is this a problem? Sure, it's impossible for us to visualise it, but mathematically it's no problem at all for anyone armed with the relevant techniques. The fourth dimension is a concept that's a century old, and has invaded the Western world's thinking in many ways. Just think of Picasso - a lot of his pictures were attempts to visualise things from the perspective of a 4-dimensional being.
Anyway, with the current superstring theories of physics there are a lot more than 4 dimensions - there are 10, 11 or 26 dimensions in this case depending on whether you're talking about basic superstrings, hetoric superstrings or M-theory. And again, these are impossible to visualise but easy to deal with mathematically.
And yeah, it's all very neat, and I'm just glad that physics is comprehensible enough that we can even attempt to understand it, let alone so that we can argue about it in places like /. :)
Even if space-time is flat across the entire universe, it is curved when there is a large amount of matter involved. This has been observed by astronomical observation, where light from distant objects is distorted by closer objects. So if space is flat, it is a pimpled surface, rather than smooth.
Gonzo
What I found most interesting, however, was the discrepancy between their estimates of Omega(baryon) = 0.05 and Omega(matter) = 0.31 (again, based on the test flight data). That means that their result requires Omega(non-baryonic) of 0.26. That is, if this result is correct there is definitely not just dark matter, but 'exotic' dark matter (WIMPs, primordial black holes, or other strange stuff) out there. Again, that's not too surprising, since primordial nucleosynthesis arguments place rather severe restrictions on how much baryonic matter there can be in the universe. Still, this gives yet another independent argument for dark matter. What's more, the amount of dark matter required is close to what is implied by galactic dynamics, which means that you have enough to explain galaxy rotation curves, but you don't have any embarrassing intergalactic dark matter. It would be a problem if there were a lot of dark matter that steadfastly refused to cluster like ordinary matter.
At the end of the day, this result looks huge. If it is borne out, then it will go a long way toward settling the question of cosmography. Then the question becomes, what to do with lambda. A nonzero cosmological constant really doesn't make any sense from a theoretical standpoint, and it brings back all of the fine-tuning problems that inflationary scenarios were supposed to rid us of in the first place. The cosmological question of the next decade will be, "What does this nonzero cosmological constant mean, and why are both it and omega so close in magnitude?" The so-called 'quintessence' models look promising in this regard. At any rate, the ball is pretty firmly back in the theorists' court.
-rpl
I've read the book and done some research into superstrings, and the answer is no. The micro dimesions called for by superstring theory are curved, but in their own separate dimensions rather than in the 4 macroscopic dimensions of "normal" spacetime. The current thinking is that these microscopic dimensions form what is mathematically known as a Calibi-Yau space, which is next to impossible to visualise without being a 6-dimension being, whereas current cosmological evidence says that the macroscopic dimensions are flat. The two have distinct curvature due to their differences in size.
Of course, it is fine to attempt to measure the curvature of the universe, but as Douglas Adams has stated in one of the Hitchhiker's Guide to the Galaxy novels (sorry, can't remember which one right now), the universe isn't really curved, but is, in fact, bent.
- Mike
"This has not, however, stopped their earnings from pushing back the boundaries of pure hypermathematics, and their chief research accountant has recently been appointed Professor of Neomathematics at the University of Maximegalon, in recognition of both his General and his Special Theories of Disaster Area Tax Returns, in which he proves that the whole fabric of the space-time continuum is not merely curved, it is in fact totally bent."
-- "The Restaurant at the End of the Universe" - Douglas Adams
- Mike
Also, the nonzero cosmological constant invalidates the BBC journalist's claim that the universe will coast to a stop at very large times. As the universe expands the matter density drops, and so a positive cosmological constant will drive the universe into exponential expansion when the matter density becomes negligible. That's assuming, of course, that the cosmological constant really is constant, which is the case in the standard cosmological models. One can imagine (and there are compelling theoretical reasons to believe) that if lambda is nonzero, then it is also nonconstant.
Finally, regarding the heat death of the universe, see the article by Adams and Laughlin in the August 1998 issue of Sky and Telescope. Apparently there will still be interesting phenomena in the universe, even after the last of the stars burn out.
-rpl
And apparently there is such thing as a "Free Lunch" ( as in beer ). We don't have to pay back the Big Bang with a Big Crunch.
The thing about this is that the Universe is a "free lunch". The positive energy of the Universe from all of its matter in whatever form is exactly balanced out by the negative energy from the potential energy of the gravitational force, and so the net energy of the Universe is zero.
Since the Universe has a net energy of zero, from the time-energy uncertainty relation h-bar >= E * t then the Universe could have been created from nothing and still exist forever without violating quantum mechanical principles. So in that repsect it truly is a "free lunch" and the question of its end is irrelevant.
Others have already pointed out the error in the earlier post - the surface of a sphere is an example of a surface with positive curvature, not negative curvature. For discussion (and a Java applet - yay) of a surface with negative curvature (in this case, hyperbolic geometry), try http://math.rice.edu/~joel/NonEuclid/.
huh? IIRC positive curvature is synclastic, while negative curvature is anticlastic. You've got it backwards.
The Universe ate my balls.
At least that was his response to me trying to explain this story. I thought it appropriate.
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Feel free to shoot me down, as it's been too many years since I was a hardcore physics geek. The curvature of our 4-D universe is often compared to a two-dimensional sheet, which could be flat, spherical, or saddle-shaped. What if the two-dimensional sheet is actually 2.4 dimensional - ie, it has fractal qualities? Does it make sense to measure the curvature of a fractal surface? Does the measurement depend on the scale that is being measured? What would the effect on cosmological theories be?
I realize that posting this question here probably makes as much sense as asking comp sci questions on alt.physics.geeks, but interesting answers to interesting questions are often forthcoming.
Draw two dots on a piece of paper. The path between the two dots with the shortest length (ie, the path in which you will expend the least ink or graphite drawing), is a "straight line". Now, draw two dots on an orange (say, at the North Pole and somewhere on the Equator), with a magic marker or something. The shortest path on the surface of the orange between those two points is some part of a great circle - part of the meridian running down from the pole to the other point. Most of the time, the path you've drawn on the orange looks curved to you, and you can imagine drilling a hole through the orange which would connect the two points as the crow flies. This is because you live (pretty much) in 3-dimensional Euclidean space.
But imagine a tiny ant or microbe on the surface of the orange - in the same way that the Earth looks flat to us, the orange would look flat to the ant. If you put some ant food (say, a drop of sugar or something) on the equator of the orange, and drop a hungry ant at the North pole, then the ant will take the shortest path it can to the food, which is along a meridian. This path looks like a straight line to the (2d) ant, but like a curve to (3d) us.
Mathematicians have a special name for a curve which takes the shortest route between two points - they call it a "geodesic". Certain theoretical physicists irritatingly call it a straight line, which can be confusing, because it's almost always not a straight line in the Euclidean sense.
Aaanyway. The special theory of relativity showed that you can't treat time and space separately - they are all wrapped up in one another in a way which only really becomes apparent if you have things travelling at high speeds. In a sense, we live in a 4-dimensional mixture of space and time, but we perceive this as 3 space dimensions and 1 time dimension which don't intermix much because you need to travel at an appreciable fraction of 600 million miles per hour to notice anything going on, and very few people ever manage to travel at a millionth of that relative to the planet's surface without ending up a bloody pulp.
So, the special theory of relativity ("SR" to its friends), says we really live in 4 dimensions. The *general* theory of relativity ("GR"), which emerged later, talks about how, in addition to time and space being wrapped up in one another, the presence of matter changes this relationship.
This is where get to spout the physics catchphrases like "Matter tells space how to curve, and space tells matter how to move".
Let's get back to the ants. Say you decide to raise a load of ants who spend their entire lives on a flat rubber sheet - the ants' idea of a straight line (quickest line between ant and food), coincides with our ideas of straight line. Now, drop a marble on to the rubber sheet - if the marble is heavy enough, it will distort the sheet. Drop a cannonball on the sheet, and you get lots of distortion. Put a drop of sugar near the cannonball, where there's lots of distortion, and you'll see the ants travelling along curves again.
Now - generalize this. Imagine a race of four-dimensional beings, who have a 3-dimensional rubber sheet on which they watch some beings who are so tiny, they usually only notice the surface of the sheet.
We are those ants.
(Sort of.)
Now, Einstein's Field equations, which you arrive at after wrestling about with some rather tedious algebra, originally took the form:
(curvature of a bit of space) = (constant) * (amount of matter in it)
Except that it was phrased in an exceedingly accurate way that boils down to sixteen smaller equations. Notice that this kind of implies that if you take away all the matter, or you travel to some region of the universe with very little in it, there's no curvature - "straight lines" are straight lines in the Euclidean sense.
Now, Einstein wasn't sure of this for various reasons, and changed the equations to read:
(curvature) = (const) * (amount of matter) + (another constant)
Where the second constant he threw in is the famous "Cosmological constant", which represents the curvature of space when you take all the matter away. If it was nonzero, it would be like you had a really saggy rubber sheet and hung it up by the corners so it was curved even if you didn't put any weights on it.
What the article suggests (as far as I can gather), is that, to a not huge degree of accuracy, this constant is zero. (Or that something else is going on - see other posts).
(Sort of. It's much, much more complicated than this, and I'm sure I'll get jumped by the local physics mafia, but I hope you get the idea.)
Apologies for the huge post, I hope it was of use to someone. If you want to read more on the subject, go for vol. 2, chapter 42 of the Feynman lectures for a very readable explanation which also involves ants, or if you want something more solid, "Essential Relativity" by Wolfgang Rindler (ISBN 0-387-10090-3) is rather good. Someone else suggested "Gravitation" by Misner, Thorne, and Wheeler, which is good and really comprehensive, but forbiddingly huge.
I often read about the universe's expansion being described as like points on a balloon being blown up, and there was no point that the universe expanded away from.
However a balloon is manifestly curved.
How does this stay consistent with the result that the universe is flat?
As for your book recommendations, they're good. For more solid texts that are more advanced than Rindler but easier than MTW, try some combination of Schutz or d'Inverno or Martin. Something at the level of Rindler would be Ellis and Williams.
Then what happens to the "place" that used to be there when one forms? How about the "places" where one has expanded (if in fact they do that) into?
Hey Rob, Thanks for that tarball!
"Going to war without France is like going deer hunting without your accordion." - Jed Babbin
A good book to read for those interested in this topic is "Wrinkles in Time" by, I think, George Smoot. It describes in novel form his work with Cobe (one of these background radiation imaging research project). He carries the story through working with Nasa, launching weatherballoons, even to antarctica. The novel is interspersed with well described information about the theories behind background radiation, the origins of the universe, and what the images they discovered really mean.
I recomend it.
This theory is based on the idea that since the universe is curved, nothing can ever travel in a truley 'straight' line, and by observing the current path of anything, we can calculate the overal curvature of the universe. There are, however, many problems with this theory leading it to be highly disputed. 1) In order to measure the true curvature of an object, you can't be on the same path as that object. So the only way to measure the universal curvature of a particle in space would be to step outside of space. 2) The theory also assumes that the universe has a constant curvature throughout it. There is no evidence anywhere for or against this. All that this 'evidence' would ever show is what the curvature of the universe is in the immediate vicinity of our galaxy. 3) you can't measure anything without effecting your results. 4) There is no way to dispute the fact that at least part of the curvature of space around us is to be contributed to the mass of objects we can or can not see. Therefore, measuring the curvature of the space around us ONLY measures the curvature of the space around us and not the entire universe
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Consciousness is not what it thinks it is
Thought exists only as an abstraction
Another question is whether the universe is finite or infinite. I think if the curvature is positive (enough), the Universe must be finite (essentially, you look at the surface of a sphere and you make the radius of the sphere become larger and larger: at some point it must decrease because of the positive curvature, and when it goes back to zero your sphere is the entire, finite, universe — sorry for the hand-waving). If the curvature is zero or negative, on the other hand, the Universe can be infinite but it can also be finite (notice that there is no difference between a finite universe and a periodic one). This applies for time as well as space.
Would you rather live in a finite universe or an infinite one?
An easy way to explain this 180 degrees, less than 180 degrees, more than 180 degrees garble is like this: Take a sheet of paper. Draw a right-angled triangle (it doesn't have to be right-angled, but this helps explain the following examples). Add up the angles. 180 degrees. Voila! This is your flat universe. Now, take the Earth. The whole thing. It doesn't have to be the Earth; it could be the sun, or a rubber ball. Pick any two points on the equator. Connect these two lines with a big pencil. Now, remember grade 4, where you were taught all longtitudnal (sp?) lines ended up at one of the poles? Well, take your two points and draw straight north from each of them. Both end up at the north pole! So you will have two 90 degree angles, plus an x degree angle. More than 180! This is a spherical, or closed universe. Now for this last one, let's take that hollow rubber ball, and cut the top half off. We're looking in on a bowl-like shape. Draw a triangle inside. The angles add up to less than 180. This is your saddle, or open universe. This makes sense, if you flatten out the earth or the open bowl. If you do this, your triangles won't really be triangles at all; your flat earth will have pushed in sides, and in the bowl the triangle's sides will stretch outwards. The theory behind the closed (spherical) universe is that, given enough mass, the universe will close in on itself, somewhat in the way in which the Earth is closed on itself. In the open (saddle) universe, there isn't enough mass, so the shape of the universe is that of a parabola (A 'U' type thing, except the sides keep moving outwards instead of being parallel). Lastly, the flat universe has a perfect quantity of mass, meaning its shape is not curved in any way. If you go from the Earth to Pluto, you're going in a perfectly straight line (well, you're really going in a straight line in whatever universe you're in; but remember, like with the triangle sides, if you are in an open or closed universe you would appear to be moving in a curved line to an outsider. This shows how in an open or closed universe, the shortest distance between two points is _not_ a straight line. This shortest distance is called a geodesic. But now I'm off topic.) In an open universe, since it does not have enough mass, the galaxies will continue to fly apart from each other, forever and ever. On the flip side, in a closed universe, eventually the force of attraction between the galaxies will be strong enough to slow down this acceleration, and the galaxies will then move back together into a Big Crunch. And again, lastly, in the flat universe, the mass of the universe is just enough to stop the acceleration apart, but not enough to start bringing it back together. Therefore, it will just stop and be still, and we'll live in a static universe. You can see how important it is, then, that we detect the enigmatic "dark matter". This invisible matter could account for up to 90% of the mass of the universe, and is really the button to whether our universe is open, closed, or flat. There is not enough detected mass in the universe to allow for a closed universe. We need dark matter. You can also see how favourable the closed universe is over the other options. A Big Crunch would give way to another Big Bang (in fact, this is not necessarily the first 'universe'; there could have already been a hundred, or a million, or infinite universes before this), and this would continue. This is the theory of the oscillating universe, and it's really preferrable to believe this as opposed to the thought of the universe going cold and dark forever. I'm personally skeptical of these findings implying a flat universe, as it just seems unlikely to have a _perfect_ amount of matter (well, it's within a range, but it's still rather precise on a universal scale) to allow for a flat universe. I'll keep my eyes open, but what I'd really like conclusive evidence of a closed universe! You don't always get what you like, though. Anyways, I just intended to explain the triangles, but I went way overboard. I guess this is just a topic that interests me! Best wishes, Mark Ferguson
You're missing my point. I'm asking a simple question here: What happens to the SPACE the singularity formed in? Take the colapse of a star for instance: What happens to the space, and more importantly, the energy and the matter that used to exist there? What happens to things in the new hole's proximity? Is that more clear?
Hey Rob, Thanks for that tarball!
"Going to war without France is like going deer hunting without your accordion." - Jed Babbin
I don't know if that's necessarily true. Whether zero or 10 to the -120th, it may not really matter either in terms of consequences or even from a theoretical standpoint. The universe's starting conditions are de facto inexplicable: they have the values they do simply because that's just the way they happened to come out in our universe. Since I know of no theory in which lambda is the result of other still more fundamental parameters, I think this might be one of those starting conditions that (putting the Cosmological Anthropic Principle aside for a moment) took purely random values.
Consciousness is not what it thinks it is
Thought exists only as an abstraction
It's certainly possible that dark matter has some sort of weird interaction characteristics that cause it not to cluster, but it's not what you expect. Particle-particle interactions are typically mediated by short-range forces, while gravity is a long-range force. In dense materials like water and oil the molecular separations are small enough that van der Waals forces and the like dominate gravity. By contrast, in space interparticle separations are large, and so interactions strong enough to separate out the dark matter would be surprising. That's not to say it can't happen (in fact, something very like that scenario happens with phenomena like ambipolar diffusion), but for it to happen on intergalactic length scales would require some creative physics. Moreover, if I recall correctly, field (i.e. away from galaxy clusters) gravitational lensing surveys put some constraints on the existence of dark clusters, so the dark matter would have to interact in such a way that it doesn't cluster at all, not even with itself. Again, one could probably work up a scenario to fit this constraint, but it's not what you expect.
Basically, it comes down to a question of parsimony. It's bad enough that the dark matter has to be nonbaryonic; one would like to stay away from anything that makes it even more exotic. Finding more mass density in the universe than can be accounted for in galaxy clusters would have required lots of new physics, and in some sense it would have undermined confidence in the standard model because when a model starts growing too many patches you start to look for something simpler. Instead the new result bolsters confidence that the standard model is basically on the right track.
I guess the short answer, then, is that nonclustering dark matter is only really "a problem" for the standard model. If the standard model is overthrown it's not the end of the world or anything. However, we like the standard model; we think we understand it pretty well, and it has a lot of useful predictive power. Consequently, most astrophysicists (including this one) would rather see it refined than discarded.
-rpl
The way many of these groups arrive at their estimate that the universe is "flat" is basically from such power spectrum measurements. Basically, the first peak of that spectrum (at an angular scale of about l=200) implies (to within reasonably small error bars) that we live in a flat universe. (More rigorously, it implies that Omega_k, an effective density term arising from the curvature, is equal to zero.)
The "power spectrum" does tell you lots of other things, true. But so does the mere fact that the CMB spectrum itself is Planckian -- it's possible to show that energy injection by unknown particle species at early times would alter the spectrum that we see today. It's also possible to constrain lots of other cosmological things, like the redshift at which reionization occurs, by observing the spectrum. This is getting more technical than is really appropriate, so I'll stop -- point is, though, that the result here (and from other similar papers) is actually pretty significant. Doesn't mean there aren't other significant papers to be written. :-)
There is more than one solution satisfying a positively curved GR universe with even curvature. One of these would be the solid surface of a hypersphere. Of course the "centre" of the hypersphere doesn't exist in our four-dimensional spacetime. But then, the throat of a wormhole or an "open" black hole doesn't exist in our four-dimensional spacetime either. Even so, it is (as you suggest) fairly unlikely that wormholes or tunnels between rotating blackholes would ever cross each other.
Consciousness is not what it thinks it is
Thought exists only as an abstraction
Frankly, this whole argument boils down to: if we can't prove the Big Bang theory completely, then we should arbitrarily except this other model here ENTIRELY ON FAITH. Oh, and I'm going to argue something random about sentiency which violates the anthropomorphic principle over and over and over.... There are many plausible theories, each with at least some evidence backing them up, about what this 99% matter is. Probably the neatest is the macroverse theory that's part of superstrings- that most of this mass is actually "leaked" from other dimensions. That may sound wacky, but believe it or not- it's a testable theory (unlike this guys version of steady state). In fact they're going to test it pretty soon...
A Universe that lasts forever and dies an entropy death kind of does not allow that.
How depressing...
It's no problem at all. According to the dominant theories:
Time is measured only from big bang to big crunch (and even then we're not sure that it keeps flowing forward during the collapse phase). Whatever, all spacetime is destroyed along with the universe at the big crunch. So, supposing an oscillating big bang cosmology: any subsequent big bang starts at time t=0 again, as if it were a replay of the original. Or - more to the point - as if it were concurrent with the original.
So sequential iterations of the big bang are exactly equivalent to completely unconnected alternate universes or alternate world lines.
However, the zero net content of the universe must cancel out (almost) exactly at the big crunch and there probably isn't going to be much of a bounce anyway. I therefore doubt that the oscillating universe was ever a realistic model, even if a collapse *was* on the cards.
Does that mean we don't get more than one go? Absolutely not. The same process of quantum fluctuation that provided our universe with a kickstart can (indeed must) have happened an infinite number of times, often resulting in a big bang.
All realities that *can* exist *do* exist, at least they do from the point of view of their inhabitants. But to the inhabitants of any specific universe, their universe and any baby universes spawned from it are all there is and all there ever will be. The siblings can never be known.
Consciousness is not what it thinks it is
Thought exists only as an abstraction
Unfortunately, your "humans are dark matter" theory has several serious problems. First, humans give off lots of infared radition (making them at least slightly luminous), and can easily be detected by telescopes (albiet only very crappy ones). Of course, if you mean human beings are floating around in space, then they'd probably be dead, meaning they wouldn't give off any radiation at all..... my god maybe you're right after all. The soylent universe! It's full of... people!
Please understand that I don't mean to be obnoxious when I say this, but it is my understanding that there is no mathematical requirement for a Calibi-Yau space to have a specific curvature (positive negative or zero).
Looking back at my post I can see how it sort of implies that, but that's not what I meant. Oh well, my poor writing skills are to blame there I suppose. Yes, the "extra" dimensions themselves are compactified into a Calibi-Yau space, but there is no requirement as of yet for that space as a whole to be curved - it is my understanding that there are a very large number of possible Calibi-Yau spaces which can be formed from compactification - selecting the correct one so that the Universe as we see it is produced is one of the major challenges of superstring theory, and one which might have to what for an underlying principle to be discovered.
Anyway, I was going to E-mail you about this but you don't have an address, so you might not get this. If you do, feel free to mail be about it. Thanks :)
In other words, give the researchers a little credit for knowing their business. It's not like they haven't thought of these things and taken them into account to the best of their (or anyone else's) ability. The have gone to great lengths to give the best estimates possible given our current understanding of physics.
-rpl