## Is the Universe finite or infinite? An interview with Joseph Silk

This interview was conducted in 2001 at ESA's European Space Technology Centre (ESTEC) in Noordwijk, the Netherlands, during an international workshop to discuss the scientific programme of the Planck satellite. Here he clarifies the concept of 'flatness', and explains why we may never get to know whether the Universe is finite or infinite.

Professor Joseph Silk

Head of Astrophysics, Department of Physics, University of Oxford, United Kingdom

Born: 1943

Savilian Professor of Astronomy, University of Oxford. Previously tenured professor at the University of California at Berkeley, United States. Currently a fellow of the American Association for the Advancement of Science, the American Physical Society and of the Royal Society, UK.

Most of his scientific research is related to the Cosmic Microwave Background and cosmology. He is author or co-author of more than 300 papers in refereed journals, as well as of many popular articles and books such as The Left Hand of Creation, Cosmic Enigmas and A Short History of the Universe.

**ESA**: The term ‘Big Bang’ suggests an explosion. But cosmologists often reject the concept of an explosion, why?

**Joseph Silk**:

Cosmologists don't like the term explosion because it conveys the idea of sound, and it doesn't make any sense to think of it like that. But apart from that, the word explosion is valid. I think that the simplest description of how the Universe originated is an explosion, in the sense that it began from a very small volume and increased very rapidly. That is usually what you mean by explosion.

**ESA**: Is the Universe finite or infinite?

**Joseph Silk**:

We don't know. The expanding Universe theory says that the Universe could expand forever [that corresponds to a 'flat' Universe]. And that is probably the model of the Universe that we feel closest to now. But it could also be finite, because it could be that the Universe has a very large volume now, but finite, and that that volume will increase, so only in the infinite future will it actually be infinite.

**ESA**: It sounds like a game of words, is it?

**Joseph Silk**:

No. We do not know whether the Universe is finite or not. To give you an example, imagine the geometry of the Universe in two dimensions as a plane. It is flat, and a plane is normally infinite. But you can take a sheet of paper [an 'infinite' sheet of paper] and you can roll it up and make a cylinder, and you can roll the cylinder again and make a torus [like the shape of a doughnut]. The surface of the torus is also spatially flat, but it is finite. So you have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat.

**ESA**: ‘Flat' seems to have a different meaning to non-scientists. By 'flat' we understand to be like a table, which has width. Does the Universe have width?

**Joseph Silk**:

Flat is just a two-dimensional analogy. What we mean is that the Universe is 'Euclidean', meaning that parallel lines always run parallel, and that the angles of a triangle add up to 180o. Now, the two-dimensional equivalent to that is a plane, an infinite sheet of paper. On the surface of that plane you can draw parallel lines that will never meet. A curved geometry would be a sphere. If you draw parallel lines on a sphere, these lines will meet at a certain point, and if you draw a triangle its angles add up more than 180o. So the surface of the sphere is not flat. It's a finite space but it's not flat, while the surface of a torus is a flat space.

**ESA**: Planck will measure the Cosmic Microwave Background (CMB), which carries information on the geometry of the Universe. Will we be able to find out if the Universe is finite or not?

**Joseph Silk**:

Even if with our Cosmic Microwave Background data we can prove that the Universe is flat, we still won't know whether it's finite or infinite.

**ESA**: Then how are we going to know whether the Universe is infinite?

**Joseph Silk**:

With great difficulty! We may never know it. If the Universe is finite, that means that in a two-dimensional geometry it would be like a torus. Now, think about a torus. In such a Universe, light travelling on the surface of a torus can take two paths: it can go around the sides but it can also go in a straight line. This means that if the Universe is like a torus, light can have different ways to get to the same point. You can have a long way and a short way. And that would not be true on a plane. But a torus means that space is more complicated. It would mean that when you measure the CMB you will see strange patterns on the sky, because the light from far away would not have come to us in quite a straight line because of the topology of the Universe. So the hope would be, eventually, to look for those strange patterns on the sky.

**ESA**: Will Planck be able to see those patterns?

**Joseph Silk**:

In principle, yes. If the Universe is like a torus you can see something. If the Universe were finite it would be 100 times larger than the horizon, which is the distance the light has travelled since the Big Bang. That would correspond to the size of the 'doughnut' of the torus. We could in principle be able to measure that with Planck. On the other hand, if the Universe was truly infinite then we would see no signal at all from this peculiar thing. What we could really say in that case is that the Universe is larger than a certain size. But if it was finite it could be measurable.

**ESA**: What would be the size of the Universe if it was finite?

**Joseph Silk**:

It could be as large as 100 times the horizon. That means that the Universe would be as much as a 100 thousand million parsecs, about 300 thousand million light years, if we could measure the topology.

**ESA**: We seem to agree that the Big Bang started with an 'inflation', a short period of high-speed expansion. But what happened before that?

**Joseph Silk**:

Maybe long before inflation there was a Universe that was collapsing near a singularity, which then inflated again, so there was already a history before the Big Bang. Some people think there was a 'pre-Big Bang'. One possibility is that this pre-Big Bang, if there was such a place, would have made lots of entropy (the amount of disorder in the Universe). And the Universe we live in does have huge amounts of entropy. That's one theory. But we have no understanding of how to change from collapsing to expanding. There's no physical way to explain that transition. Some people believe that they have explanations the pre-Big Bang, so it's a respectable theory.