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A heavy ball rests on a trampoline, and the fabric sags beneath it. Any rolling ball nearby inevitably rolls toward the center. This is roughly how gravity works on the scale of the entire Universe. But what if the fabric were arched upward, like a dome? Then the ball would tend to roll outward. This simple difference between concavity and convexity turns out to be the key to the question of whether the Universe can exist forever without a moment of birth.

The authors of the new study dissected the equations of expansion of the universe and checked what happens to the energy of light crossing the cosmos from end to end. In a flat or open world, resembling an infinite plain or a saddle, the total energy of such a ray always goes negative. It's as if the trampoline were forever pulling everything toward itself. To compensate for this effect, one would have to add matter with negative energy, which does not exist in nature. Therefore, an eternal flat Universe is impossible: it would either collapse or be born from a superdense point.

The researchers constructed concrete examples of such eternal closed worlds, filled with an ordinary scalar field (the simplest kind of matter that uniformly fills space). It turns out that positive curvature acts like a spring, preventing the Universe from either collapsing to a point or flying apart into emptiness. Moreover, if one mistakenly tries to describe such a Universe as flat, one might think it contains a mysterious dark energy with peculiar properties. But this effect is tiny — only about a percent given current constraints on curvature.

So geometry dictates fate. If our world is indeed flat or open, it had a beginning. If it is closed, it could have done without beginning or end. And then it continues its eternal dance, held by its own curvature, like that very ball on the elastic fabric.