Imagine a universe in which you could point a spaceship in one direction and eventually return to where you started from. If our universe were small in size, such movements would be possible, and physicists could measure its volume.
“We could say: We now know the size of the universe,” astrophysicist Thomas Buchert of the University of Lyon, Center for Astrophysical Research in France, said in an e-mail to Live Science.
By studying light from the earliest Universe, Buchert and a group of astrophysicists concluded that our cosmos could be multi-connected, meaning that space is closed in on itself in all three dimensions, like a three-dimensional donut.
Such a universe would be finite, and, according to their results, our entire cosmos could be only three to four times larger than the limits of the observable universe, which is about 45 billion light years away.
Physicists use the language of Einstein’s general theory of relativity to explain the universe. This language relates the contents of space-time to the twists and curvatures of space-time, which then tell these contents how to interact. This is how we experience the force of gravity.
In a cosmological context, this language relates the contents of the entire universe–dark matter, dark energy, ordinary matter, radiation, and everything else–to its overall geometric shape.
For decades astronomers have argued about the nature of this shape: whether our universe is “flat” (meaning that imaginary parallel lines will always remain parallel), “closed” (parallel lines will eventually intersect), or “open” (these lines will diverge).
This geometry of the Universe dictates its fate. Flat and open universes will continue to expand forever, while a closed universe will eventually collapse on its own.
Numerous observations, especially of the cosmic microwave background (a flash of light that occurred when our Universe was only 380,000 years old), have firmly established that we live in a flat Universe. Parallel lines remain parallel, and our universe will continue to expand.
But shape is not just geometry. There is also topology, which is how shape can change while still retaining the same geometric rules.
For example, take a flat sheet of paper. It is obvious that it is flat – the parallel lines remain parallel. Now take two edges of this paper and roll it up into a cylinder. These parallel lines are still parallel: Cylinders are geometrically flat. Now take the opposite ends of the cylindrical paper and connect them. You get the shape of a donut, which is also geometrically flat.
Although our measurements of the content and shape of the universe tell us about its geometry-it is flat-they do not tell us about its topology. They don’t tell us whether our universe is multi-connected, which means that one or more of the dimensions of our cosmos are connected to each other.
While a perfectly flat universe would extend to infinity, a flat universe with a multi-connected topology would have a finite size. If we could somehow determine that one or more dimensions spiral into themselves, then we would know that the universe is finite in that dimension. We could then use these observations to measure the total volume of the universe.
A team of astrophysicists from the University of Ulm in Germany and the University of Lyon in France turned their attention to the cosmic microwave background (CMB). When the CMB was obtained, our Universe was a million times smaller than it is today, so if our Universe is truly multi-connected, it was much more likely to collapse in on itself within the observable boundaries of space.
Today, because of the expansion of the Universe, it is much more likely that the folding is occurring at scales beyond the observable boundaries, and so it will be much more difficult to detect folding. IGB observations give us the best chance to see the fingerprints of a multiply connected Universe.
The research team paid particular attention to perturbations – a fancy physical term for shocks and oscillations – in the CMB temperature. If one or more of the dimensions in our universe joined together, the perturbations could not be larger than the distance around these loops. They simply would not fit.
As Buchert explained, “In infinite space, perturbations in CMB radiation temperature exist at all scales. However, if space is finite, there are no wavelengths that are larger than the size of space.”
In other words: There is a maximum size of perturbations that can reveal the topology of the universe.
The MDB maps produced by satellites such as NASA’s WMAP and ESA’s Planck already reveal an intriguing number of missing perturbations at large scales. Buchert and his colleagues investigated whether these missing perturbations could be caused by a multi-connected universe.
To do so, the team ran many computer simulations of what CBM would look like if the universe were a tri-torus, the mathematical name for a giant three-dimensional donut in which our cosmos is connected to itself in all three dimensions.
“So we have to run simulations in this topology and compare it to what is observed,” Buchert explained. “The properties of the observed CMB fluctuations show ‘missing power’ at scales larger than the size of the universe.”
The lack of power means that CMB fluctuations are not present at these scales. This would mean that our universe is multi-connected and finite at these scales.
“We find a much better fit to the observed fluctuations compared to the standard cosmological model, which is considered infinite,” he added.
“We can vary the size of the space and repeat this analysis. As a result, we will get the optimal size of the universe that best agrees with the CMB observations. The answer of our work is unequivocal: a finite universe fits the observations better than an infinite model. We can say: Now we know the size of the Universe.
The team found that a multi-connected Universe about three to four times larger than our observed bubble best fits the CMB data. Although this result technically means that you can travel in one direction and end up where you started, in reality you can’t.
We live in an expanding universe, and on a large scale, the universe is expanding at faster than the speed of light, so you will never be able to catch up and complete the cycle.