As a child, one often wonders how large the Universe actually is. Does it continue forever in every conceivable direction? Our brains, understandably, have a hard time coping with infinity. Everything in our everyday lives, including really big objects like our entire planet, is of finite size.

So maybe it feels easier to handle the idea of a Universe of finite size. But if the Universe is of finite size, must there be some kind of “boundary”? But what is beyond that limit? More space and more stars? The unintuitive strikes back with force.

But in the natural sciences – not least in astrophysics – we are forced to leave our intuitions early. How the entire Universe works is not governed by our own emotional and intuitive requirements. So the question of the size of the Universe must be answered by comparing different models with observations of the Universe.

### The models that do not match observations are thrown away

Before 1917, however, there were no elaborate models of the entire Universe to throw away or keep. Cosmology – the study of the Universe as a whole based on well-established physical principles – was not yet developed. Einstein had only a few years earlier developed his new theory of gravity, his general theory of relativity.

According to the new theory of gravity, space and time (space-time) are curved by matter and energy! A massive object, e.g. a star, space-time curves more than a lighter object, such as a planet. In the curved space around a massive object, less massive objects can orbit, much like a ping-ball that goes in an “orbit” around the curved surface of a trampoline created by a bowling ball.

What happened in 1917 was that Einstein used his general theory of relativity to formulate a model that describes the Universe as a whole, and not just individual objects within the Universe. In Einstein’s model of the Universe, the Universe is not infinitely large. Oddly enough, the new theory of gravity allows a Universe of finite size! But how is it going?

Is there any “limit” in his model or what? Amazingly, the answer is no!

Matter can, as mentioned earlier, curve the space-time. If there is enough material then you can get the whole Universe so curved that it forms something of a three-dimensional sphere. What this means is that if you decide to travel in any direction long enough, you might return to the place you started from! In this case, the Universe is extremely large, yet of finite size and contains a finite number of stars (the idea of other galaxies had not yet been accepted).

However, there was a problem. According to Einstein’s equations, a static Universe is unstable.

It probably starts to expand or implode to a point. Instead of accepting it, Einstein introduced something he called a “cosmological constant” (and what we now often call the dark energy).

The cosmological constant wants the Universe to expand, while the gravitational pull of stars wants the Universe to implode. The two effects are mutually exclusive in Einstein’s model, and we get a static Universe of infinite age.

It was also later found1 that this is also unstable as the slightest movement of matter causes an imbalance that causes the Universe to either expand or implode. In addition, astronomers in the late 20th century began to discover that galaxies are moving away from us in all directions. The universe thus expands. So it had turned out that Einstein’s tranquil Universe did not describe reality. However, the general theory of relativity had foreseen that the Universe should probably expand or implode, for which there was now evidence.

The new evidence of a Universe that is growing and is dynamic gave rise to the birth of modern cosmology. Enthusiastic models that could describe the Universe were derived. Everything from models where Universum cyclically undergoes expansion and contraction to models where Universum expands faster and faster, or different quickly in different directions. They also began to spend a lot of time trying to “weigh” the Universe. By determining the masses of galaxies, one could try to estimate the size of the Universe.

A Universe filled with relatively little matter is infinitely large – infinitely larger than what we can see with our best telescopes. In fact, our best telescopes can only capture light that has had time to reach our telescopes. It may sound obvious. But that means that if the Universe is of finite age then we will also observe a finite part of either a finite or infinitely large Universe.

This is the reason why the starry sky is relatively dark and not dazzling (often called Olber’s paradox). If the Universe is extremely much larger than the “little” part we can see, and we had the opportunity to see so far, the night sky would be so densely populated by stars and galaxies that we would not have much of a “night” left.

Since we can only observe a small (or large?) Part of the Universe as a whole, we cannot be sure whether what we see here is representative of the Universe as a whole. It is for the same reason that one cannot come to the conclusion that the Earth is flat because the Earth appears to be flat locally.

But we assume that the part of the Universe we can observe with our telescopes is relatively typical. And with that assumption and our “weighing” of matter and energy in the Universe, we can conclude that the Universe as a whole is much larger than the part we can see with our best telescopes. The latest measurements of the Planktelescope indicate that the Universe is very “flat” to high precision. What this means is that the Universe is very close to a boundary case where, on the one hand, it is spherical and of finite size, and on the other hand has negative curvature (like a saddle) and is of infinite size.

The conclusion we can only draw from is that the Universe is unimaginably large – big enough that in most cosmological calculations one can assume that the Universe is infinitely large.

If one uses Planck’s measured parameters and more, the Universe should have a circumference of at least ~ 1,000 billion light-years (which can be compared to the visible Universe that has a radius of ~ 46 billion light-years)! 2 So even if the Universe is of finite size there is no reason to have claustrophobic thoughts. However, the question of what is beyond our horizon, and how large the Universe actually is, remains unanswered.

In theoretical cosmology, for example, there are suspicions that we live in a “multiverse”, where our “universe” is just a bubble – paradoxically, an infinitely large bubble in an infinitely large sea of infinitely many such bubbles (headache, anyone?) – of many. This idea is still relatively speculative even though it is based on a fairly accepted theory of the early Universe (inflation).

You want to test this by searching for “bruises” in the cosmic background radiation from the early Universe.3 Finding one or more “bruises” would indicate one or more collisions with other universes. This would mean that we would have to further enlarge our perspective, which has been a general trend since the beginning of modern science.

Interesting times lie ahead of us with great potential discoveries that put our planet and our unrest in a larger and richer perspective. Right now we cannot put a number – which is probably so large that we have difficulty comparing it to anything concrete – of the size of the Universe. We have to settle for the fact that the Universe is a huge place.