What shape is the universe?

May 12, 2015 by Vanessa Janek, Universe Today
Geometry of the Universe. Credit: NASA/GSFC

The universe. It's the only home we've ever known. Thanks to its intrinsic physical laws, the known constants of nature, and the heavy-metal-spewing fireballs known as supernovae we are little tiny beings held fast to a spinning ball of rock in a distant corner of space and time.

Doesn't it seem a little rude not to know much about the itself? For instance, if we could look at it from outside, what would we see? A vast blackness? A sea of bubbles? Snow globe? Rat maze? A marble in the hands of a larger-dimensional aliens or some other prog rock album cover?

As it turns out, the answer is both simpler and weirder than all those options. The shape of the universe is a question we love to guess at as a species and make up all kinds of nonsense.

Hindu texts describe the universe as a cosmic egg, the Jains believed it was human-shaped. The Greek Stoics saw the universe as a single island floating in an otherwise infinite void, while Aristotle believed it was made up of a finite series of concentric spheres, or perhaps it's simply "turtles all the way down".

Thanks to the mathematical genius of Einstein, cosmologists can actually test out the validity of various models that describe the universe's shape, turtles, mazes, and otherwise.

There are three main flavors that scientists consider: positively curved, negatively curved, and flat. We know it exists in at least four dimensions, so any of the shapes we are about to describe are bordering on Lovecraftian madness geometry, so fire up your madness abacus. Ya! Ya! Cthulhu ftagen.

A positively curved universe would look somewhat like a four-dimensional sphere. This type of universe would be finite in space, but with no discernible edge. In fact, two distant particles travelling in two straight lines would actually intersect before ending up back where they started.

You can try this at home. Grab a balloon and draw a straight line with a sharpie. Your line eventually meets its starting point. A second line starting on the opposite side of the balloon will do the same thing, and it will cross your first line before meeting itself again.

This type of universe, conveniently easy to imagine in three dimensions, would only arise if the cosmos contained a certain, large amount of energy.

To be positively curved, or closed, the universe would first have to stop expanding – something that would only happen if the cosmos housed enough energy to give gravity the leading edge. Present cosmological observations suggest that the universe should expand forever. So, for now, we're tossing out the easy to imagine scenario.

It’s a reasonable question to wonder what the shape of the Universe is. Is it a sphere? A torus? Is it open or closed, or flat? And what does that all mean anyway?

A negatively curved universe would look like a four-dimensional saddle. Open, without boundaries in space or time. It would contain too little energy to ever stop expanding.

Here two particles traveling on straight paths would never meet. In fact, they would continuously diverge, getting farther and farther away from each other as infinite time spiraled on.

If the universe is found to contain a Goldilocks-specific, critical amount of energy, teetering perilously between the extremes, its expansion will halt after an infinite amount of time,

This type of universe is called a flat universe. Particles in a flat cosmos continue on their merry way in parallel straight paths, never to meet, but never to diverge either.

Sphere, saddle, flat plane. Those are pretty easily to picture. There are other options too – like a , a doughnut, or a trumpet.

A soccer ball would look much like a spherical universe, but one with a very particular signature – a sort of hall of mirrors imprinted on the .

The doughnut is technically a flat universe, but one that is connected in multiple places. Some scientists believe that large warm and cool spots in the CMB could actually be evidence for this kind of tasty topology.

Lastly, we come to the trumpet. This is another way to visualize a negatively curved cosmos: like a saddle curled into a long tube, with one very flared end and one very narrow end. Someone in the narrow end would find their cosmos to be so cramped, it only had two dimensions. Meanwhile, someone else in the flared end could only travel so far before they found themselves inexplicably turned around and flying the other way.

So which is it? Is our universe an orange or a bagel? Is it Pringles? A cheese slice? Brass or woodwind? Scientists have not yet ruled out the more wacky, negatively curved suggestions, such as the saddle or the trumpet.

What shape is the universe?
WMAP data of the Cosmic Microwave Background. Credit: NASA

Haters are going to argue that we will never know what the true shape of our universe is. Those people are no fun, and are just obstructionists. Seriously, let us help you get better friends.

Based on the most recent Planck data, released in February 2015, our universe is most likely… flat. Infinitely finite, not curved even a little bit, with an exact, critical amount of energy supplied by dark matter and dark energy.

I know this gets a little confusing, and meanders right up to the border of nap time, but here's what I'm hoping you'll take away from all this.

It's amazing that not only can we make guesses at what our incredible universe looks like, but that there's clever people working tirelessly to help us figure that out. It's one of the things that makes me happiest about talking every week about space and astronomy. I just can't wait to see what's next.

So what do you think? Is a flat universe too boring for your taste? What shape would you like the universe to be, given the wide array of options?

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Explore further: Is the universe a hologram?

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not rated yet May 12, 2015
It seems, though, that the flat universe requires such a critical balance, that a minute, random, quantum energy fluctuation would quickly tip it into one of the alternative configurations. A flat universe is so wildly unlikely, even if it is momentarily flat, it wouldn't stay that way for very long. At least, that is my take. On the other hand, a universe with an enormous radius of curvature would appear flat to any observer. Most likely, then, the universe is either open or closed but the dimensions are so great, no observation is likely to tell us which alternative is the correct one.
May 12, 2015
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not rated yet May 12, 2015
richardwenzel: recall too that the other possibility, a negatively curved surface with very low magnitude of curvature, also exists.

One can turn the same question on its head of course... why so close, but not precisely zero? What cosmic coincidence would create that situation? Simply saying the odds are low for one configuration or the other isn't a terribly great argument given the data we now have.

Perhaps, in the future, we'll know something more about the nature of dark energy or dark matter that lends us a strong argument for the "precisely zero" curvature. Perhaps in the distribution of energy to the various fields of the universe, it had to be done in such a way as to balance out.

My money, however, is on an open and negatively curved universe which just happens to be presently passing through an eon of relative flatness.
5 / 5 (4) May 12, 2015
@Ren -
They do not seek for answers on the right place
-right... let's just all give up and go back to playing patty-cake with camel-shit.
not rated yet May 13, 2015
Flat eh, where have I heard that before?
5 / 5 (1) May 13, 2015
It seems, though, that the flat universe requires such a critical balance, that a minute, random, quantum energy fluctuation would quickly tip it into one of the alternative configurations.

Well, if you think about it then, in an enclosed universe, _something_ has to be constant at some level. Might as well be curvature. (An alternative would be a three -or more- force equilibrium which is just unlikely)
From such a constant you can derive that any local deviation requires some sort of counteraction - otherwise you get a runaway effect. Such local deviations would then be (local) breaks in symmetry
not rated yet May 13, 2015
Sounds like a sort of conservation law, conserving whatever must be constant to preserve curvature. Any adjustment would have to be "local" as well, since no information can propagate above light speed. An adjustment would have to take place within the forward lightcone of the deviation. But if there were no conservation of curvature, a change of curvature triggered by some local quantum deviation could only propagate at light speed. And, since a quantum fluctuation sufficient to change flatness to one of two alternatives could take place anywhere in the universe and in multiple locations, we end up with a crazy quilt, a universe with closed and open curvatures propagating at light speed from many locations-- what a mess!
not rated yet May 13, 2015
Although, now that I think of it, a mechanism like this could result in many bubble universes, some open and some closed, since the critical quantum fluctuations would have taken place very early, very soon after the Big Bang. Heck, maybe they WERE the BB!
not rated yet May 13, 2015
Reading the paper, I think it is in bad shape locally.
1 / 5 (3) May 16, 2015
The Laws of Conservation of Energy require energy distribution systems follow the guidelines Einstein elucidated in his General Relativity which I have partially reproduced below:

Part III: Considerations on the Universe as a Whole
Albert Einstein 97

If we are to have in the universe an average density of matter which differs from zero, however small may be that difference, then the universe cannot be quasi-Euclidean. On the contrary, the results of calculation indicate that if matter be distributed uniformly, the universe would necessarily be spherical (or elliptical). Since in reality the detailed distribution of matter is not uniform, the real universe will deviate in individual parts from the spherical, i.e. the universe will be quasi-spherical. But it will be necessarily finite. In fact, the theory supplies us with a simple connection between the space-expanse of the universe and the average density of matter in it.

1 / 5 (1) May 16, 2015
The volume of the cosmos is that of a doughnut. The matter in it, travels in a circular helix.
not rated yet May 16, 2015
Just who are these "haters" you refer too? Could it be those who hold religious views? While I am a non-believer myself, I consider such remarks as hate speech and little short of intolerance. You should find a better group of "friends".
1 / 5 (3) May 17, 2015
He quotes about "haters":

"Haters are going to argue that we will never know what the true shape of our universe is.Those people are no fun, and are just obstructionists"

.....he's saying the "haters" are those who believe we can't know the true shape of the U.

Then he states:

"Based on the most recent Planck data, released in February 2015, our universe is most likely… flat. Infinitely finite, not curved even a little bit, with an exact, critical amount of energy supplied by dark matter and dark energy."

..........so based on his eclectic blending of theories about an interpretation of Planck Data, & hypotheses of DM & DE, he's bragging that he's got all the answers concluding that the Universe is infinitely flat, and if you disagree with him you are a "hater", so I guess that makes Einstein one of his "haters", me too I guess, I loath Einstein because he set forth in his General Relativity just the opposite of the funny farm science this guy has come up with.

1 / 5 (1) Jun 14, 2015
Filtration of the theories and filtration of minds -present state of cosmic Confusion prevailing today.
cosmology needs revision -cosmic consciousness helps to search through origins-Vedas Interlinks
This state predicted in my book -is a reality now.OM COSMIC CONSCIOUSNESS TO COSMOLOGY REVISION-2000( TXU 982-559) Pages 94, Fig 16-author vidyardhi Nanduri

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