As if the universe couldn’t provoke more questions—what is its topology? Scientists say it's flat, and so would Euclid. Let me explain.
Whether the universe will stop or even reverse the expansion that started with the Big Bang probably keeps at least some insomniacs up at night. Why is understandable. The possibilities, from a finite universe to an infinite universe to a constant déjà vu of expansion and retraction that could send galaxies rocketing out into wild space just to come crashing back into each other and inciting another epic explosion, could possibly make you lose your mind.
So why should knowing the universe is flat help you sleep at night?
Think of a square room (it can be your gaming room or your personal shrine to Star Trek—no one will know). Walk around the corners and you’ll realize you’ve made four 90-degree turns to come back to where you started. In Euclidian geometry, you can say it’s flat. This is because the topology of the surface you’re walking on determines what happens after a turn. Now think that, instead of padding around in your Cthulhu slippers, you’re piloting a spaceship into the deep unknown. No matter how many light-years away you are, you’ll still need no more or less than four 90-degree maneuvers to find yourself back where you first blasted through the Earth’s atmosphere. Sound familiar? That’s because the topology of the universe is flat.
Cosmic microwave background (CMB) radiation is the lingering aftermath of the Big Bang. The expanding universe cooled enough to release photons, then stretched these photons and shifted them to the microwave spectrum, 2.7 degrees above absolute zero. Astronomers have been able to observe the slightest variations in CMB temperatures with ultra-sensitive space telescopes. It’s like viewing a scale model of the observable universe. Meaning, what looks like an infinitesimal region that varies slightly in temperature can be an immense cluster of galaxies. Also meaning, these temperature variations would appear majorly distorted (see above) if the universe were anything but flat.
“Flat” translates to 90-degree turns like those you made with your imaginary spaceship always behaving like 90-degree turns. Parallel lines will stay parallel. Everything seems sane until you realize we still have no idea whether the universe is finite or infinite. A finite universe would have measurable curvatures, something that science can’t yet prove or disprove, since its volume is believed to be at least 100 times more than what we’re able to observe. Emphasis on at least.
Astronomers believe that a flat universe must have been flat when it was a dense singularity in the distant past, and has remained flat for 13.8 billion years, a stretch of time almost unfathomable to the human brain. Now, that should keep you wide awake.