(Intro)

Matter distorts the universe.  It's the fundamental idea behind Einstein's theory of general relativity.  Every black hole, every star, every space rock, bends small bits of space-time, like a bowling ball on a trampoline.  But if certain areas of the universe can be curved, so can the universe as a whole, which leads to a major question: how does the overall amount of stuff in the universe curve it?  In other words, what is the geometry of the universe?  

The possible answers are surprisingly uncomplicated.  The universe can either have a positive curvature, a negative curvature, or it can be flat with no curvature, but figuring out which one of those is true is a little more involved.  When you zoom out really far, like, on the order of 300 million light years, the universe looks the same from every point in space, which means the universe's overall geometry must be the same everywhere, too.  This doesn't make it any easier to picture what it means for 3D space to be flat or curved, because human brains can't perceive things from some external fourth spacial dimension, but we can try.

Really, it comes down to what happens when you draw a triangle connecting three points and add up the angles between them.  If they equal 180 degrees like in a regular triangle you'd draw on a piece of a paper, you live in a flat universe.  Scientists modeled that with a flat infinitely long plane.  If the angles of the triangle add up to more than 180 degrees though, you live in a positively curved universe.  This is where things get harder to picture, but it's like each side of the triangle is bending outward.  You can get an idea of how this happens by connecting three points on a sphere.  Instead of straight lines, each side of the triangle curves along the sphere, and we end up with a set of bigger angles.  That's positive curvature.  Negative curvature is the opposite.  It's like the sides are bowing inwards and the angles come out to be less than 180 degrees.  This (?~1:56) with a kind of saddle shape.  

Unfortunately, the universe is just too big for us to actually test this out.  It's like how the Earth's surface feels flat beneath our feet even though it's positively curved.  We could  never be able to tell if the sides of the triangle were bending, but there are other methods we could use to figure out the universe's geometry.  It all depends on how much matter and energy is out there curving space-time.  It's divided into three main groups.

The first and probably the most obvious is matter.  That includes all the matter we know and love, like protons, neutrons, and electrons, as well as dark matter, which we can't detect visually, but we know is there because of its gravitational pull.  There are also a lot of mass-less photons and nearly mass-less neutrinos flying through space at or near the speed of light.  They get their own group, and finally, there's dark energy, the mysterious stuff that's making the universe expand more quickly.  That's pretty much all we know.  Hey, we're working on it. 

Estimates put dark energy at comprising somewhere around 75% of all the stuff in the universe right now, but figuring out the geometry caused by these ratios is easier said than done.  It all centers around the critical density: the exact amount of stuff you need in the universe for it to be flat.  If the real density is less, the universe will have negative curvature.  If it's more, we're in a positively-curved universe, and the thing is, we don't know the exact critical density.  It depends on both the strength of gravity as well as how fast the universe is expanding, and we're still working on exact numbers for the latter.  We've gotten really close to exact numbers though.

Cosmologists can get a very precise estimate of how fast the universe is expanding using things like supernovas or temperature fluctuations in the radiation left over from the Big Bang, and in 2015, researchers used data from the Planck Space Telescope to get a similarly precise estimate of the real density of the universe.  Even when you take into account the margins of error, the real density is so close to the critical density that cosmologists are pretty confident we live in a flat universe.  So no bendy triangles!

Of course, the universe's geometry doesn't affect us on a day-to-day basis, but it does help answer one of the fundamental questions of existence: how will the universe end?  If there were no such thing as dark energy, the curvature itself would doom our reality to one of two fates.  If we lived in a positive universe, everything would eventually collapse back in on itself, and the universe would end in what cosmologists call the big crunch.  If the universe were negatively curved or flat, the universe would continue expanding forever, and everything would end in ice, not fire, but with any amount of dark energy, the story gets more complicated.  

Luckily, astronomers have made charts.  These charts include a couple of new hypothetical fates, like a big bounce, where instead of starting with the Big Bang, the universe would switch between expanding and contracting when it hit a certain minimum size, but with current measurements, the universe looks like it had a clear start and will end, just not with a bang, although it won't end with a whimper either, because the sound wave wouldn't be able to propagate through that vacuum, and if you're interested in learning more about that, you can check out the episode about the end of everything on the main SciShow channel.

In the meantime, thanks for watching this episode of SciShow Space.  For more videos on the weirdness of the universe and everything space, just go to YouTube.com/SciShowSpace and subscribe.

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