What Shape is the Universe?

 

 

It's the biggest thing there is. So big we can't see all of it. Even trying to imagine what it *would* look like is difficult...

The universe. By definition, all that exists. Space itself, going on seemingly forever, much further than we can see even with our most advanced telescopes. What we do NOT know about the universe far outweighs what we DO know, and this raises some very interesting questions:

What shape is the universe?

Is it a big ball?

Is it curved?

Is it flat?

What is outside the universe?

How big is it?

Is it infinite???

Where is the edge?

Where is the centre?

Is it expanding?

What is it expanding into?

..... and many more.....


The first thing we have to consider before trying to answer these questions is to remember that there is a distinction between the observable universe and the entire universe.

THE OBSERVABLE UNIVERSE

We can look up at the sky at night and see stars, some just a few light years away. Sirius, the brightest star in the sky, is 8.6 light years away. One light year is the distance that light travels in one year: 9.46 trillion kilometres (9,460,000,000,000 km), so Sirius is 81 trillion km away from Earth.

Betelgeuse, the red giant star that marks the right shoulder of Orion, is more than 600 light years away, so its light takes much longer to reach us.

The Andromeda galaxy is further still, 2.2 million light years away, but this can also be seen without a telescope.

The light from these objects takes years to reach us - in some cases, hundreds, thousands or millions of years - so we are seeing them as they were in the past, but most stars and galaxies are billions of years old, so this distance does not make a lot of difference. Those stars and galaxies -probably- still exist and still look the way we see them. If a star such as Betelgeuse explodes as a supernova today, we would know nothing for another 600 years.

With telescopes we can see even further. The galaxy GN-z11 is currently the most distant object we can see, 32 billion light years away.

Beyond the visible spectrum, we can see further. The cosmic microwave background (CMB) is radiation emitted from the first matter ever to exist, the quark-gluon plasma, 380,000 years after the Big Bang (more than 13 billion years ago). This radiation fills the whole universe, and by measuring its temperature and redshift (the lengthening of its wavelength as the universe expands), we can determine that it is reaching us from a distance of 46.5 billion light years. This marks the radius of the observable universe.

So what is beyond the 'observable'? We do not know because we cannot see any further. All we can see is light which has had time to reach us. From their redshift, we know that the most distant objects are all receding away from us. It is likely that there are more galaxies beyond the 'horizon' - and, as time passes, light from those galaxies will eventually reach us.... But there is a complication. And it's a very strange one...



THE UNIVERSE IS EXPANDING FASTER THAN LIGHT

 

It sounds wrong, but it is true.

For every megaparsec (one million parsecs or 3.26 million light years), an object we see is moving away from us at 68 kilometres per second. Therefore a galaxy two megaparsecs away is receding at 136km/s; a galaxy three megaparsecs away is receding at 204 km/s, etc. etc...

If you keep on adding those megaparsecs you eventually pass 300,000 kilometres per second, which is faster than light.

Hold on, you say - I thought NOTHING was faster than light!

Well, -almost- nothing. To be more precise, nothing with mass can reach -c- (the speed of light in a vacuum, 299,792,458 metres per second). But this does not apply to the expansion of the universe because it is -spactime itself- which is expanding.

Those distant galaxies are not - "locally" - travelling faster than light. They are not overtaking nearby photons. If you were in one of those galaxies and looking back at the Milky Way galaxy, you would see exactly the same thing: --this-- galaxy would be racing away from you at superluminal velocity.

The universe as a whole is expanding, but because the universe is so big we only notice this in the huge distances between very distant clusters of galaxies.

This is why the age of the universe (13 billion light years) does not co-incide with the radius of the observable universe (a much bigger 45.6 billion).


THE COSMOLOGICAL PRINCIPLE

A very common question that pops up when we talk about the universe expanding is: What is expanding INTO? What is OUTSIDE the universe?

This is where it gets weird. And very interesting...

Remember the cosmic microwave background? It fills the entire sky. Not only that, it is the same temperature no matter which direction we look in. There are some slight variations in temperature, but those variations are fairly uniformly distributed. The CMB looks pretty much the same no matter which part of it you look at.

A common misconception about the Big Bang is that it was an explosion that threw energy and matter outward in a huge expanding sphere, and our galaxy is somewhere within that spherical region of space. This model would put the location of the Big Bang at the central point of that explosion.

But it was not an explosion of energy or matter; it was an expansion of spacetime itself.

It was not an expansion IN space, but an expansion OF space.

If it had been an explosion located in one region then its afterglow - the CMB - would only be visible in one part of the sky. But it is not, it is radiating towards us from EVERY direction.

There is no centre. Also, there is no edge. The universe is not a three-dimensional region of space contained within a larger region of space. It is, from our perspective of being inside it, the whole of space AND time. In that sense, there is no "outside" (and no "before").

This brings us to the cosmological principle: the large-scale spatial distribution of matter in the universe is isotropic and homogeneous...

Isotropic: It looks the same in every direction

Homogenous: It looks the same from every location

Again, this makes no sense to us intuitively. But this is what we observe. The CMB is isotropic and homogenous and - on a grand scale - so is everything else.

ANCIENT GALAXIES

The very distant galaxies are all receding away from our galaxy in a uniform pattern of increasing velocity. Look north and a galaxy one megaparsec away is flying away at 68km/s. Look south at another galaxy one megaparsec away and it will be flying away in the opposite direction at the same speed.

That's not all. Spectroscopy shows us the chemical elements present in those galaxies. The further away they are, the fewer elements they have heavier than lithium. Why is that? Because the further away they are, the older they are. We are looking back in time across billions of years.

The Big Bang was an expansion of spacetime which contained all of the energy now present in our universe. It was concentrated in a very small region at first, so it was in a state of extreme density and energy. As the universe expanded it gradually began to cool and the first subatomic particles (quarks, gluons, electrons, photons, etc.) formed. These then formed the first atoms, but only the three simplest elemements: hydrogen, helium and lithium.

Stars formed from these (mostly hydrogen atoms), forming heavier elements in their cores. When some of these stars exploded as supernovas they seeded space with these heavier ("metallic") elements, which in turn became the next generation of stars (and planets, comets, etc.).

So, from our perspective, it looks as if the Big Bang happened RIGHT HERE and the universe is expanding with us right at the centre. But this is a 3D visualisation that does not reflect the actual data. Ever since Copernicus we have accepted that Earth is NOT the centre of the cosmos. Our viewpoint is not special. Earth orbits an average yellow star at a random distance from the centre of a fairly average galaxy... Why should we think that our perspective on a greater scale is any less average?

The matter density of the universe is homogenous on a cosmic scale, which makes it highly unlikely that we just happen to be in the centre. There is nothing else 'special' about our little corner of space. This means that, for an observer in any one of those distant galaxies, they seem to be in the centre with all other galaxies - including ours - flying away from them.

So which one is "really" receding? The answer is: All of them. On a cosmic scale, all galaxy clusters are moving away from each other.

Imagine baking a cake full of raisins. As the cake bakes it expands and every raisin moves away from every other raisin...

CURVED SPACE

 

This is all very disorienting.

Even the cake analogy is not perfect because we are still visualising the universe in three dimensions. What is outside the cake???

These questions are based on a misunderstanding of the nature of space itself. We tend to visualise things intuitively, based on our past experience of living in our everyday world..... but our intuition misleads us because our experiences are limited to the conditions of living on the surface of a planet. The cosmos at large behaves in much stranger ways.

Walking to the shops, we move around in space. It seems to be a big empty area of..... well, nothing really. A big, three-dimensional classical/Euclidian volume, intuitively natural and predictable, that goes on forever in every direction. In this category of space, parallel lines never meet. The angles of a triangle always add up to 180° because it is "flat" (zero curvature).

But ever since Einstein came up with general relativity, we know that this is not the whole picture...

Space is elastic. In the presence of mass it curves, and we call this curvature gravity. Not only that, it curves time as well (speeding it up), because space and time are one phenomenon.

So when we think about the universe we cannot just visualise it as a big region of static 'nothingness', we have to take its elastic nature into consideration. We cannot just assume that it is "flat" (uncurved) in a three-dimensional way as it appears to be.

The space we move through looks "flat" to us but it is definitely curved. If it was not, we would float away from the ground. Gravity is that "inward" curvature.

To use a more extreme example, think of a black hole. Light cannot escape once it passes the event horizon, but not because gravity is 'pulling' on the light. The light is still moving in a straight line but it is like a straight line drawn on a curved surface.

It cannot come out of the black hole because space is curved to such an extreme extent that the only direction is inwards. Just like there is no such thing as north of the North Pole, inside a black hole the direction 'out' simply does not exist.

So is space still curved away from the Earth?

Generally, yes. Gravity is everywhere in space, holding the planets in orbit around the Sun, holding the stars together within the galaxy, holding the galaxies together in groups and clusters. This is positive curvature.

But that is not the whole picture, because as we discussed earlier, the galaxies on a grander scale are moving away from each other, in opposition to gravity. This is negative curvature.

So in answering the question about the shape of the universe we have to know if - on balance - the curvature is positive, negative or zero.

In a flat universe (zero curvature, like the surface of a sheet of paper) the angles of a triangle always add up to 180°.

In an "open" universe (negative curvature, like the surface of a saddle) the angles of a triangle add up to less than 180°.

In a "closed" universe (positive curvature, like the surface of a sphere) the angles of a triangle add up to more than 180°.

So how do we answer this question? By looking at the most distant thing we can see; the cosmic microwave background. As discussed, it is largely homogenous (uniform/smooth). We would not see this smoothness if it was curved. The measurements taken in recent years (by, for example, the Planck space observatory) gives us a very closely zero value ( with a 0.4% margin of error).

Some of the data, however, may indicate positive curvature ( a "closed" universe). It seems there is more gravitational lensing than we expected to find. In a closed universe a straight line in any direction will eventually curve back and meet itself, like drawing a straight line on the surface of a sphere....


INFINITE???

 

Many times you will hear people talk about the universe being infinite, but this is not an actual established fact.

Could it be infinite? It is certainly possible but it would be difficult to prove this. First of all, remember that we cannot see all of it. We cannot measure what we cannot see. If we *could* see all of it, that alone would give it a finite nature.

A flat, infinite universe (Euclidian space) has no boundaries, so if this was the case it would have no edge and no 'outside'. But could does that mean that a finite universe must have a boundary/edge?

Actually, no. Imagine you are walking on the Moon. Pick any direction and you can keep walking forever (infinitely) but the space itself - the surface of the Moon - is NOT infinite.

Remember the raisin cake? The cake itself expands as it bakes and all the raisins move away from each other, but it left us with the question: what is outside the cake?

We have to think beyond three dimensions. Now the cosmos is the surface of a balloon. Dots on the surface represent galaxies. As the balloon inflates its surface increases and the distance between the dots increases. The surface is expanding but it has no edge and no centre. A two-dimensional spacecraft travelling along this surface can keep going in one direction forever without finding an edge, but the two-dimensional space it is moving through does not, itself, go on forever.

That might sound like an overly complicated picture, but it is actually a more simple one than trying to imagine a universe with a boundary. If we try to imagine a boundary it raises the questions: what does the boundary look like? What is outside the boundary? If there is something outside, does THAT have a boundary? And so on and so on... All of which are unnecessary without the initial assumption.

This model of the universe is known mathematically as a closed manifold. You can imagine the cosmos as a the three-dimensional surface of a four-dimensional hypersphere.

It is a very odd image but it gets us closer to the physical reality, or at least as close as we can visualise it.

We will probably never know everything about the physical properties of the universe, including its shape, but understanding what we DON'T know - and how our intuitions and preconceptions can very often mislead us - is sometimes a good place to start.

SCIENCE & SPACE