Traveling in space is one of man's oldest dreams, but what if we could travel to the farthest reaches of the Universe? Would we continue to move forward indefinitely in a straight line without ever stopping? Or would we return to where we started after a while?
When Man thought that the Earth was flat, it was unthinkable to imagine that by moving in a straight line, we could end up returning to our starting point. However, today, this fact is indisputable:traveling in any direction in a straight line without ever stopping over a distance of 40,000 km invariably brings the traveler back to his point of origin.
It is a logical observation knowing that, geometrically, the Earth is finite but without edges. For the Universe, the question may also arise. It is possible to imagine an infinite Universe that would perpetually expand in all directions. But it is also possible to think of a finite Universe, the observational clues collected over the last few years not allowing us to definitively rule on the question.
Same topic:
What is the total size of the Universe?
The Universe could possess a multi-dimensional structure and have the geometry of a hypersphere or a hypertorus, in which the different dimensions are closed and finite, curving back on themselves. If so, then traveling in a straight line long enough would bring us back to where we started. Looking long enough (and not aging), it would even be theoretically possible in this case to see the back of our head via the light emitted from our point of origin.
To know if the Universe actually has this geometry, it is necessary to look, on large scales, for regions of the cosmos that seem to display identical properties in different directions. A finite and recurring universe implies the repetition of identical structures.
Although it is difficult to observe such a recurrence (since the finiteness of the speed of light implies that we would observe the same objects but at different stages of their evolution), there are nevertheless always a small number of objects which appear at the same evolutionary stages in different places. None of these repeating identical structures appear in the large-scale Universe, but that's not the only place we can look.
The cosmic microwave background (CMB) also represents a candidate for study. The fluctuations of the latter show a very particular pattern:they follow a bell curve distribution, with a slightly higher amplitude on large scales. There is another singular characteristic of the CMB:the fluctuations show a random distribution of this particular pattern.
Several powerful algorithms have been developed for the purpose of searching for repetitive and non-random signals or correlations between fluctuations in different parts of the sky. If the Universe were finite and self-enclosed — leading to repeats of its structures and regions — the cosmic microwave background would necessarily contain the evidence. However, no such clue was found in the CMB.
This absence of repetitions does not mean that the Universe does not have this topology. It simply means that if the Universe is repeating itself, if it has a closed hypersurface, that is only visible on larger scales than we can currently observe. Since we are limited by the distance that light can travel in 13.8 billion years, there are not many avenues left to explore on the distances available to us.
However, even if the Universe is finite, it will be impossible for us to travel in a straight line to return to our starting point, regardless of the technological level reached by Man. In view of the acceleration of the expansion of the Universe, it is already physically impossible to reach the borders of the observable Universe. Unless the Universe repeats itself on scales less than 15 billion light-years in diameter, it will be impossible for us to experimentally validate this back-to-origin hypothesis.
This physical impossibility does not prevent the Universe from being finite and closed on itself like a hypersphere or a hypertorus. It only means that the acceleration of the expansion of the Universe prevents us from performing a complete revolution of the Universe. In conclusion, it is a combination of:the finite age of the Universe, the finite speed of light in vacuum, the expansion of the Universe and the presence of dark energy.
Everything we can infer comes from observations made in the observable Universe. For the moment, the data collected seems to indicate that the Universe is flat, non-repetitive and potentially infinite. Future observations over greater distances may finally indicate the presence of a curvature that was previously inaccessible to us.
