Cosmology FAQ Part 3 (The Present)

Some time ago, in a not-too-distant place, I did a 'Cosmology 101' on Periscope, an exciting endeavour in which I tried to answer the 25 most common questions in cosmology. It was long, it was dense, and it was great fun. If you missed it, don't worry, you can read this series of posts, which will cover the same topics.

In Part 1 we covered the Big Bang; the beginning. Part 2 dealt with what's happened since then: 13.8 billion years reduced to one post. Today we will discuss what the universe looks like now.

This series of posts will have a lot of information. If you don't understand everything the first time, don't worry. This is just to give you an idea of the type of topics we can discuss in this blog. If you see anything mentioned here that you would like to know more about, or that you think is unclear, let me know in the comments; that will give me ideas for things to talk about or write about in the future.

So what is the current state of out universe?

9. What is happening to the universe now? 
Ever since the Big Bang the universe has been growing and cooling down. Our evidence shows us the universe is 13.8 billion years old, and the current temperature of the CMB (Cosmic Microwave Background) is T$=2.725$K, which is -270° Celsius, and if you use the weird scale, it's -455° Fahrenheit (seriously though, why do you use this scale?).
Our best model for the universe is the $\Lambda$CDM model. This means the universe is governed by dark energy ($\Lambda$ - pronounced 'lambda'), and cold dark matter. When we say cold dark matter we mean the dark matter is moving slowly - so slow that we don't need to consider relativistic effects. The most recent data tell us the universe contains 5% normal matter, 25% dark matter and 70% dark energy. And that leads us to a very obvious question.

10. What is dark energy, and what is the cosmological constant?
We are not sure what exactly this dark energy - or cosmological constant - is. We are very sure the expansion of the universe is accelerating (I'll come back to this), and we know something must be causing everything to go outwards, despite the attractive pull of gravity, which means it has to have negative pressure. The first person to come up with a valid, and testable, explanation for dark energy could win a Nobel Prize.

The Einstein Field Equations, with $\Lambda$

Historically, the cosmological constant dates back to Einstein. When he formulated general relativity, the universe was thought to be static: neither growing nor shrinking. If this was the case, why didn't the universe collapse due to the gravitational force? Einstein's response was to put a cosmological constant in his equations.

Turns out this guy was right

This fixed the issue, but a few years later the expansion of the universe was discovered, meaning the cosmological constant was no longer needed. Einstein removed it from his equations, and often referred to it as his 'biggest blunder'. In the 1990s it was seen, however, that the expansion of the universe was accelerating. It wasn't just expanding, it was doing so quicker than before. This meant we once again needed some form of 'anti-gravity' in our equations, and so we put the cosmological constant back in. Seems like Einstein was right again.


11. What do we mean by expansion? Are objects moving away from us, or are our definitions of length and time are changing?
By expansion we mean that everything is moving away from everything else; the distance between galaxies is increasing (see question 14).

Case 1: Grid points get further apart

We could consider expansion from two different points of view. Imagine we draw a grid on the universe, and mark galaxies at different points. In our first scenario we fix the galaxies at specific grid points, and these grid points get further apart, causing redshift as they do. If before there was 1 million lightyears between the galaxies, after a certain amount of time there are 1.5 million lightyears.

Case 2: Grid points are fixed

In our second scenario, we keep the grid fixed, and let the galaxies flow freely. As time passes, we notice the galaxies move away from each other, also causing redshift. Like before, the distance between the galaxies has increased (and if my two drawings are correct, you can see that the increase in distance is the same in both scenarios). Both of these points of view are equally valid, and in fact general relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views.

Notice that in the above example, in both scenarios the definitions of length and time are not changing: one small square on the paper is always 0.5 million light years. This is not like when we changed our definition of a planet to kick Pluto out; the definitions of length and time are constant. The distance between two galaxies, however, is not constant: it is gradually increasing.

12. Why do we think that the expansion of the Universe is accelerating?
Imagine you are looking at a 60 watt light bulb. The light bulb always emits the same amount of energy, but if you walk away from it, you notice it gets fainter and fainter. This is because the amount of light you see depends on the distance, even though the amount of light emitted by the bulb is the same. With this idea, you could calculate the distance to the light bulb based on how much light you see. In astronomy we do something similar; we look for objects that emit a well-known amount of light, which we call standard candles. Specifically, we use supernovae: the violent deaths of stars. The amount of energy emitted by a supernova is extremely well know. This means that if we measure how bright the supernova appears to us, we can measure its distance from us, the same as the light bulb.

Redshift and apparent magnitude of supernova. Credit: U. Alberta

The next thing we do with these supernovae is measure their redshift (using their spectral lines), which tells us how much the universe has expanded since the light left the supernova. If the expansion of the Universe is accelerating, the expansion was slower in the past, and the distance to a supernova now would be larger than it would be in a non-accelerating case. If the expansion is decelerating, it was faster in the past and the distance now would be smaller. What we found is that in far away galaxies supernovae appear fainter than expected; therefore they are further away than they would be if they were moving at a constant speed.
If you are travelling in a car at a constant speed of 50 kilometres an hour, after one hour you should be 50 kilometres away. However, if you are 80 kilometres away, it means at some point you increased your speed: you accelerated. The same is true for the universe: if the distant galaxies are further away than expected, they must have accelerated.

13. Can objects move away from us faster than the speed of light?
As always when relativity is involved, the first thing we have to ask is 'from whose point of view?'. Things are relative, after all. Special relativity tells us that two objects cannot pass by each other with relative velocities faster than the speed of light. This is fairly straightforward, the problem comes when we try to apply this to objects very far apart. Then we have to ask who is measuring the distance between the objects, who is measuring their velocity, and if this observer is moving. I'll dedicate a whole post to special relativity in the future. To answer this question, let's assume that the distance to a galaxy is the distance between us at a specific time, measured by a set of observers moving with the expansion of the universe (so in the rest frame of the moving galaxy), and all making their observations when they see the universe as having the same age (the age of the universe also depends on who is looking). In this specific case, velocity of this receding galaxy can definitely be larger than the speed of light. This does not contradict special relativity, because we are not talking about the relative velocity between two objects as they pass each other.

Related to this question, we could ask if the universe is (or was at some point) expanding faster than the speed of light. The short answer is no, the long answer can be found on Sean Carroll's blog.

14. Why doesn't the Solar System expand if the whole Universe is expanding?
The objects in the Solar system are under the constant influence of gravity. Gravity pulls objects together, but it doesn't have effect across large distances. Mathematically, the gravitational force decreases with the distance squared. This means that if we get ten times further away, the gravitational force is a hundred times weaker. Imagine there is a constant battle between the gravitational force pulling objects inwards, and the expansion of the universe pushing objects away. On small scales, such as solar systems (or indeed galaxies), gravity wins, but on large scales the expansion of the universe wins. This also explains why galaxies can collide: on the 'small' scales of galaxies gravity wins, on large scales of the whole universe dark energy wins.

As an analogy, imagine two marathon runners: Bob (gravity) and Lisa (expansion). Bob decides to sprint and try to last as long as possible, while Lisa decides to maintain a calm and steady pace. At the first checkpoint, Bob will be in front of Lisa, but as the race goes on, Bob will lose energy and slow down. By the end of the race, Lisa will likely be winning. On small scales, Bob wins, but on large scales Lisa wins.

15. What is the Universe expanding into?
Nothing! The idea that the universe is expanding into something is a common misconception; we imagine the universe to be in something. I often use the analogy that the expansion of the universe is like a cake in the oven rising. However, the universe is not in anything. The universe is defined as everything in existence: if we were expanding 'into' something, it would imply there is something outside of the universe, but by definition, this would also be part of the universe. This is why we can't talk about 'the edge of the universe'. On a similar note, if the universe has no edges, we say it's infinite (see question 17).

Even if there was something that we are expanding into, it's not something we would have any access to; we have no way of exchanging information with it, so it's not a profitable thing to think about. We are asking about the 'external' geometry of an object in which we are 'trapped'. It's like putting wheels on a tomato: time consuming and completely unnecessary.

16. What is the observable universe? How big is it?
Einstein taught us that the speed of light is not infinite; it has a clearly defined value of 300,000 kilometres per second. The age of the universe is also quite well known. This means that light has only been able to travel a certain distance since the beginning of the universe. This brings us back to the idea of observable universe. The observable universe is everything we are able to see in the universe; it's a sphere centred around each observer. Everyone is the centre of their own observable universe. The light from objects beyond our observable universe hasn't yet had time to reach us.

The size of the observable universe often leads to misconceptions: one could naively assume that as the universe is 13.7 billion years old, the observable universe would have a radius of 13.7 billion light years. This is wrong! The light that we see from a star emitted 5 billion years ago was 5 billion lightyears away when the light was emitted, but the star has moved away from us since then, due to the expansion of the universe. Taking into consideration this expansion, current estimates put the size of the observable universe at 46.5 billion light years in radius, so 93 billion light years in diameter.

Earth's size compared to the observable universe. Image by Andrew Z. Colvin

17. How big is the universe? How can something that started of so small be infinite?
We believe the universe is infinite, but we really have no way of testing what's outside our observable universe. It would take light over 93 billion years to cross the observable universe (even more if we take into consideration expansion), which is a lot. The observable universe might not be infinite, but it is ridiculously big, and we think our observable universe is only a small fraction of the whole thing.

Now we need to make a slight distinction: I've said before that at the Big Bang, everything was contained in a small point. Of course, what we mean is that everything in the observable universe was concentrated into a small point: we can't make the same claim for things outside of the observable universe, at least not without a model to tell us exactly what the universe looked like when gravity and quantum mechanics worked together; for that we need a theory of quantum gravity.
But what we do know is the universe is big. Very big. So big that we can justify saying it's infinite.

18. Is the universe flat? What does that mean?

The universe is homogeneous (same in every direction) and isotropic (same from wherever you look). Mathematically, there are only three possibilities for a universe like this; flat like a sheet of paper, hyperbolic like a Pringle, and spherical like a ball.
This can be seen by drawing triangles: on a flat surface the sum of the angles in any triangle is always 180°. On a negatively curved surface (like a crisp/potato chip) the sum of the angles in a triangle is smaller than 180°. On a positively curved sphere the sum of the angles in a triangle is more than 180°. Our universe is flat; triangles in the universe will look the same as triangles on a sheet of paper.

From a more physical point of view, general relativity explains that mass and energy bend the curvature of spacetime, so the curvature of the universe is related to its density (mass over volume). We use something called the density parameter ($\Omega$), which is defined as the density of the universe divided by the critical energy density: the mass energy needed for a universe to be flat. So our three cases reduce to the following: if $\Omega>1$ the universe looks like sphere, if $\Omega<$ the universe looks like a crisp, and if $\Omega = 1$ the universe is flat. Our measurements show that the density parameter is really close to 1. In fact we find that the universe is flat with only a 0.4% margin of error.


So we've seen that our universe is flat, undergoing accelerated expansion, and filled with a lot of stuff we don't understand. We've covered quite a few questions today; but there is a lot to say about the universe.
In the fourth, and final, part of this series we will discuss the big questions like the fate of the universe.

The UCLA has a nice (but outdated) FAQ about the universe. See it here.