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.
as written by the authors arXiv:2605.18965
We study the relation between geodesic completeness, the averaged null energy condition (ANEC), and spatial curvature in Friedmann--Robertson--Walker (FRW) cosmology within classical general relativity. Using the affinely parameterized ANEC along radial null geodesics, we prove that non-static flat or open FRW spacetimes in the regular classes considered here cannot be both null geodesically complete and ANEC-satisfying. Bounded oscillatory or cyclic flat/open models do not circumvent the obstruction: the negative affine-ANEC bulk term accumulates over infinitely many cycles, giving \(I_{\rm ANEC}=-\infty\) for non-static periodic cases. Equivalently, within these classes, non-static ANEC-satisfying flat or open models are null incomplete. The sign obstruction is absent in closed \((k=+1)\) FRW geometry, where the positive curvature term enters the affine ANEC identity with the opposite sign and can support nonsingular, geodesically complete cosmologies with ordinary NEC-respecting matter. We give explicit closed-FRW scalar-field constructions, including a fully analytic quadratic reconstruction and a cubic-root reconstruction in closed quadrature, and contrast them with their flat realizations, which require NEC-violating support. Furthermore, we quantify how positive curvature can bias flat-model reconstructions toward an effective phantom equation of state, finding only a percent-level effect under current curvature bounds. The result is a curvature classification of ANEC-compatible eternal FRW cosmology: flat and open branches are obstructed, while the closed branch admits explicit complete realizations, with global de Sitter appearing as the vacuum limiting representative.
If our Universe were closed and the size of a soccer ball, a beam of light emitted in one direction would return to you from behind, having looped around the entire cosmos.
In Keith Laumer's novel "Worlds of the Imperium," heroes travel between parallel universes, some of which are closed into a ring: there you can walk forward and arrive in the past.