The part of the Universe we can observe appears perfectly flat: this implies, among other things, that going straight ahead infinitely, one would never return to their starting point.
The idea of a finite Universe without boundaries may seem strange, but just like the surface of our planet, the Universe could be limited in size and have no edge, being curved in on itself. In that case, a journey in a straight line could, in theory, return to its starting point.
To determine the shape of the Universe, scientists rely on the cosmic microwave background, a relic light from the earliest ages of the cosmos. By analyzing the temperature patterns in this fossil glow, they determine the curvature of space. Current data indicate that, within the limits of our field of view, the Universe appears flat, which corroborates theoretical expectations.
This measured flatness does not necessarily reveal the complete shape of the cosmos, however: very distant regions, beyond the reach of our instruments, could exhibit twists or connections.
If our cosmic horizon represents only a tiny fraction of the actual size of the Universe, provided it is finite, then we might measure it as flat when it is not. Just as the Earth's surface seems flat if you only measure it over a few yards (a few meters).
If a curvature exists, it could manifest at scales much larger than our observable region, thus remaining beyond the reach of our tools.
Flat geometry does not rule out elaborate topologies. For example, a cylinder or a Möbius strip are geometrically flat but have wrapped shapes. In the Universe, one or more dimensions could close in on themselves while maintaining a flat appearance, which would allow for intriguing arrangements like Hantzsche-Wendt spaces.
Despite extensive investigations, including the search for duplications in the cosmic microwave background, no evidence of a closed topology has been found. For now, the Universe appears both flat and simple in its structure. But the unknown beyond the cosmic horizon means that this supposed flatness could remain unproven.
The cosmic microwave background
The cosmic microwave background is a fossil light that has been traveling for nearly 14 billion years. Emitted when the Universe had cooled enough to become transparent, it provides a snapshot of the first moments. By mapping its tiny temperature fluctuations, scientists reconstruct the distribution of matter in that distant era.
These temperature patterns are compared to theoretical predictions to estimate the geometry of space. If the Universe were curved, the apparent size of these fluctuations would be altered by the trajectory of the light. Current observations show excellent agreement with a flat model, supporting the idea of a Universe with no detectable curvature in our observable environment.
The cosmic microwave background was identified by chance in the 1960s and has since transformed cosmology. It provides precise limits for parameters like the expansion rate of the Universe and the amount of dark matter. Thanks to dedicated space missions, its mapping is becoming more detailed, improving our view of cosmic history.
Thus, this radiation provides a valuable perspective on the origins of the Universe, helping to confirm or rule out theories about its structure. Technological advances continue to increase our information, making the cosmic microwave background a pillar of cosmological research.
The topology of the Universe
Topology is a mathematical discipline concerned with the general shape of objects, regardless of their deformations. Applied to the Universe, this amounts to asking whether space contains hidden loops or connections. Even with a flat geometry, topology can introduce arrangements like cylinders or Möbius strips, where moving in a straight line could return you to the starting point.
In a Universe with a closed topology, some dimensions close in on themselves. For example, if one dimension is circular, by moving far enough in one direction, one would return to their starting point. This does not affect local geometry, which can remain flat, but it modifies the global nature of space. Models include shapes such as the three-dimensional torus.
Cosmologists evaluate these concepts by examining the cosmic microwave background or the distribution of galaxies. They look for pairs of identical objects appearing in opposite directions of the sky, a possible sign of a looping Universe. So far, no such duplication has been spotted, indicating that the observable Universe is topologically simple.
In the absence of proof, the exploration of cosmic topology continues. It allows for considering Universes with unusual configurations, like Hantzsche-Wendt spaces, which involve hexagonal tilings.