Sunday, 30 January 2022

New home

After over six years, the livestreaming show Cup of Cosmology has a new home, and so this blog is also moving. Going forward, all content (old and new) both for the livestreams and the blog can be found at (The new site goes live at 19:00 CET on 30/01/22.)

It's an exciting new stage, there's going to be more shows, more guests, more interaction with everyone, more ways to get involved... and more blog posts!

All of the old blog posts here will gradually be migrated to the new site. For now, the Brain Teaser Wednesday archive will stay here.

Thank you for being part of Cup of Cosmology over the last years, your support means a lot to me. I hope you'll join me in the next step of this journey on!

Sunday, 21 May 2017

The Big Bang Model

The Big Bang Theory is one of the pillars of modern cosmology, so it's about time I dedicated a blog post to it. The Big Bang (BB for short) is many things, but before we get into that, it's useful to first remember what it isn't.

What it isn't
A TV series. There is no laugh track included in this blog post, I'm afraid.
On a slightly more serious note, one of the most common misconceptions about the BB is that it's a theory about the origin of the universe. The BB model is often accused of "not explaining what caused the bang, or what came before the bang", but the Big Bang theory never claimed to be able to explain these things; that's not its purpose. That's like asking a coffee machine to make you toast. If you do want toast (or an answer to the question of what came before the Big Bang), you might find something useful on the FAQ post. No toast here though, only coffee.
Another misconception about the BB model is the "bang" part. Despite the misleading name, the Big Bang model does not involve an actual bang; there was no initial explosion, but there was - and still is - an expansion taking place everywhere in the universe at the same time.

Okay, so what is it?
13.8 billion years of history in one image.
The BB theory explains the evolution of the universe from an initial singularity until today, and makes predictions for what we can expect in the future. That means the BB model covers more than 13.82 billion years of cosmic expansion, which is rather impressive. In very early times, the universe was in a really hot, really dense, and really small state. We refer to this as the initial singularity, or "Big Bang". The theory doesn't start at this singularity, though, as a singularity is just a fancy way of saying "our equations break down at this point". Our model begins a fraction of a second after this initial singularity, and moves forward with it. The BB theory explains that the universe has been gradually expanding and cooling down, going from this hot, dense, and small initial state to the massive, complex, and rather chilly place that it is today.

This cooling down and expansion is a lot more significant than it might sound, though. As the universe cooled down, the first particles could begin to form. Initially, the universe was so hot that everything was a bit chaotic: the particles were constantly interacting, but not forming lasting bonds. Dark matter particles, always the more elusive of the bunch, broke away at an early time and went their separate way to start setting up the scaffolding for future structures.
Gradually, the temperature cooled down enough for "normal" (baryonic matter) particles to bind together and form the first nuclei. First came hydrogen nuclei, and through Big Bang Nucleosynthesis - which is very similar to what happens inside stars - heavier nuclei like Helium and Lithium could form. With more expansion and cooling down, electrons could combine with the nuclei to form the first atoms - which also caused the photons (particles of light) to break away, to later become the cosmic microwave background radiation.
Filaments of dark matter on large scales, with galaxy clusters
at the intersections. From Springel et al, Millennium Simulation
These initial hydrogen atoms could coalesce into the first stars, and with enough stars in one place, the first galaxies could begin to form, and later galaxy clusters. But these galaxies didn't just form anywhere; the dark matter that broke away at an earlier time had a strong gravitational effect, causing the stars and galaxies to form in a giant structure we call "cosmic web". All of this could happen thanks to the expansion and cooling of the universe, and all of this is described by the Big Bang theory.

Why should I believe it?
As any good scientific theory, the Big Bang model has a lot of observational evidence backing it up. The expansion of the universe was first measured by Hubble in the early 20th century. Hubble noticed that distant galaxies move away from us faster than closer galaxies. Since then, we have increasingly precise measurements of the movement of galaxies, which all seem to indicate an expanding universe. We've also been able to measure that this expansion is accelerating, but that's a whole other blog post.
Furthermore, the abundance of the light elements (like Lithium and Helium) should be set by the Big Bang Nucleosynthesis, and can be calculated. We can measure the amount of these light elements in really distant galaxies in early stages of evolution, where there hasn't been enough time for more of these elements to form. The results of these measurement match what we expect from the BB model.

But a theory is not complete without predictions. The biggest prediction made by the Big Bang model is the the Cosmic Microwave Background radiation (CMB), which is a bath of photons everywhere in the universe, made up of the photons that broke away when the first atoms were formed. These photons have been propagating freely ever since, growing fainter and less energetic due to the expansion of space (if their wavelength increases over time, their energy decreases). The accidental discovery of the CMB in 1964 by Penzias and Wilson, which led to a Nobel Prize in 1964, was the key piece of evidence which made the Big Bang model the prevailing cosmological theory.

Not perfect, but the best we have
With all the evidence we have, we know that the Big Bang theory is the best model we currently have to understand the universe. However, despite its overwhelming success, there are a few aspects of the universe that seem at odds with the Big Bang Model.

  • Horizon problem: The photons of the CMB have the same average temperature of 2.73 Kelvin (-270 Celsius), varying by no more than one part in 10000. This means that if we measure CMB photons coming from opposite directions, they will be at the same temperature, despite being separated by more than 28 billion light years. As nothing can travel faster than the speed of light, these photons have not been able to communicate in any way, and given how far apart they are now, they weren't in causal contact (close enough to affect each other) in the early universe. This poses the question of why are all of the photons at the same temperature? 
  • Flatness problem: We have very good measurements on the shape of the observable universe, and our latest data show us that the universe is flat (if you are wondering what we mean by a flat universe, check out question 18 in the FAQ page). The shape of the observable universe is given by its density, and this could take any value, yet of all the possible values, the density is exactly the one that is needed to have a flat universe. This seems like a fine-tuning issue, and rises the question of why is the universe so flat?
  • Monopole problem: Electricity and magnetism present a certain duality, and can in fact be grouped together under the umbrella term "electromagnetism". We have single electric poles -or charges - in the form of electrons. However, no single magnetic charge - or monopole - has ever been found, despite being predicted by several particle physics models. Of course, it could be that the models predicting these magnetic monopoles are wrong, but it is also interesting to wonder if there is a deeper explanation to why we haven't yet found these monopoles. 

Given these questions, what do we do with the Big Bang model? Unanswered questions are usually not a good thing in scientific theories. But don't worry, the Big Bang theory is safe: we know how to solve these issues! We just need to introduce something known as inflation, which will be the focus of a future blog post.

Friday, 7 April 2017

FameLab: 3-minute science slam

Well, it's been a while. Hello everyone, and welcome back to Cup of Cosmology! This post will not have much scientific content, instead it's intended to bridge the gap between "no posts in almost a year" and "back to (hopefully) regular posts".

First of all, thanks for coming back! I know I haven't posted in a very long time, and I apologise for that; despite my best intentions there were always things getting in the way of blog posting, some of which I'll tell you about in this post.

Despite not being active on the blog, I have been doing some science communication stuff, mainly with my weekly Periscope broadcasts. I'm usually on every Sunday at 16:30 CET, unless I'm travelling, which I have been doing a lot lately. Do you have a question about cosmology? If so, join me any Sunday and ask away. I probably can't answer any cosmetology questions, though feel free to try.

Apart from my own periscopes, I've managed to get several people from the Institute for Theoretical Particle Physics and Cosmology (TTK for short) involved in periscopes as well. You can join the conversation any Wednesday at 18:00 CET, and sporadically on other days as well. There are some great people involved, so you should definitely check it out if you haven't done so already.

Finally, I'd like to tell you about something interesting I did a few weeks ago: FameLab.
FameLab is an international science communication competition, in which scientists have three minutes (only!) to present a topic related to their research. The only props allowed are the ones you can carry on to stage yourself: no slides, no setup time, and no textbooks. I took part in the Germany Regionals, and I tried to explain cosmological perturbations (there will be a blog post on this topic at some point) using a slinky toy. You can watch my video here:

Not seen in the video: the approximately 400 members of the audience. I've always been nervous of public speaking, so this was a big challenge for me. In the end, I really enjoyed it, and despite not progressing to the next round, I feel like I learnt a lot. A few years ago, getting up on stage and doing a science slam seemed unimaginable to me. I know I wouldn't have found the courage to do it without all of the support and encouragement from everyone on Twitter and Periscope, so thanks to you all for helping me with this.

Well anyway, that's enough about my recent activities, let's talk about the future! I plan on going back to my weekly Sunday Periscope discussions on my account, and I have some good ideas for the TTK account: hopefully we'll have more guests and specific topics soon. As for this blog, I intend to start posting more regularly now. I am preparing posts about the Big Bang, the CMB, inflation, perturbations, dark matter, and many more. If you have any suggestions for topics you'd like me to cover, please let me know in the comments.

Enough rambling, there's science to be done! Expect another post soon.

Saturday, 16 April 2016

Special relativity and time dilation

Now that we know what a theory is, we can tackle one of the biggest theories in physics: general relativity, Einstein's masterpiece. We should, however, start with special relativity to prepare the playing field a bit. This post (and the next one) will be a review of the things we discussed on Periscope recently. There will be some maths, just in case you want to check the numbers I give, but you can happily skip all the maths and still understand what I'm saying.

In order to understand Einstein's theories, we need to understand the context in which he developed them; which means we need to start with Newton.

1. Newtonian gravity
Newton invented calculus, a law of
gravity, and ridiculous hair styles.

Newton, as well as inventing calculus, came up with an idea in 1687 that was revolutionary for his time: things fall down. But they don't just fall down, they fall towards each other. Specifically, he realised that any two objects in the universe - no matter how big or small or how far away they were - would attract each other via a gravitational force, as long as they had mass.

This gravitational force is attractive, universal, proportional to the mass of the objects, and inversely proportional to their distance. Which means the closer together and the bigger the objects are, the more gravitational pull they feel.

That is why we are stuck on the surface of our planet: Earth is huge and very close to us, so it attracts us. The Sun is huge and relatively close to Earth, so it keeps Earth in a stable orbit. Gravity is also very weak, which is why something as small as a magnet can pick up a paper clip that is being held down by the whole planet's mass.
Newton's law of gravity was, and still is, very useful for describing gravity in everyday life, but it had it's problems. The first problem Newton encountered was that he couldn't explain why gravity exists, nor how it could affect things at a distance. It also had serious problems explaining the movement of things that travelled really fast, such as light beams. It was incomplete, but it was the best he could come up with in his time.

2. Special relativity
In the second half of the 19th century, scientists were trying to find an aether; a mysterious medium through which light (and gravity) propagated. In this point of view, the laws of physics would depend on how people moved relative to this aether, despite the fact that this contradicted experiments. Then along came Einstein to shake things up a bit, he decided to accept the experimental results as true, and modify the theory, and in doing so he removed the need for an aether.

The first concept we need to understand is that there is no such thing as absolute motion; everything moves relative to one another. As an example, imagine you are on a train travelling at 100 km/h. You could quite happily argue that you are at rest, and everything else is moving. If you were to throw a ball out of the window at 10 km/h in the direction the train is moving, you would see the ball as moving at 10 km/h. An observer outside the train, however, would see the ball moving at 110 km/h, as they would have to add on the speed of the train. Motion depends on the observer; it depends on the frame of reference from which you measure.

Next we can introduce the concept of inertial frames of reference: these are just systems that move at constant velocity, with no acceleration. If you are in a car travelling at 50 km/h constantly, you are in an inertial frame. However, when you slow down at a traffic light, you are changing your speed, so you are no longer in an inertial frame.

Armed with these pieces of knowledge, we can now formulate the postulates of special relativity, as Einstein did in 1905. Note that a postulate is something we use to build a theory; they are facts that have been proven to be true, but we don't necessarily need to know why they are true.
  1. The laws of physics must be the same in all inertial frames of reference (thus eliminating the idea of an aether).
  2. The speed of light in a vacuum is the same for all observers, regardless of the velocity of the source/observer.
These postulates matched all the observed phenomena, and changed the way people thought about motion. From these two postulates, we reach an obvious conclusion: the idea of simultaneity is relative. If you measure two events as happening at the same time, it doesn't necessarily mean other observers will also see these events happening at the same time. Einstein had a useful thought experiment to illustrate this. Imagine you are on a moving train (at a constant speed!), standing directly at the centre, and you fire two laser beams in opposite directions.

You will see the laser beams reach the ends of the carriage at exactly the same time, as seen in the image on the top. An observer outside the train, however, will see the train as being in motion, so for them the light beams will not reach the ends of the carriage at the same time. This is because from their point of view, the light beam moving in the direction of travel has a greater distance to cover, because it has to 'catch up' with the movement of the train, as seen in the bottom image.

The next big question we need to ask ourselves is how can the speed of light be constant? Let's imagine we are on separate rockets, and for now we'll work from my frame of reference. My rocket is at rest, and your rocket is moving past me at 0.5c (half the speed of light). In your rocket, you are bouncing a light beam off two mirrors; one on the ceiling on one on the floor of your rocket. You will measure the light beam as travelling at the speed of light. From my frame of reference, I will also measure the light beam as travelling at the speed of light, even though the light is travelling a greater distance (because the mirrors are 'running away' from the light beam at the speed the rocket is moving.

Image source: How to: Special Relativity
In the above image we can clearly see that from my point of view, the light beam has a greater distance to travel. Velocity is always defined as distance
travelled over time it takes, so if you and I measure the same velocity, but a different distance, something else also has to change. Specifically, the time it takes to make the journey also has to change.

3. Time dilation in special relativity
If we impose that the speed of light has to be constant, and different observers see light travelling different distances, the clocks must also tick differently. This is the main idea of time dilation: time does not pass the same for people moving at different speeds. Recovering our example of the rockets above, if you are travelling at 0.5c, I will see clocks on your ship as running slower. By the time I've seen your clocks tick one second, mine will have ticked 1.15 seconds. You will still feel time as running normally, but I will see time passing slower for you.

We can see some specific examples of this if we look at the formula on the right: if I see you travelling at 0.5c, one second for you is 1.15 seconds for me. If you are travelling at 0.9c (90% the speed of light), one second for you will be 2.3 seconds for me. If you travel at 99.9% the speed of light, one second for you is 22.3 seconds for me. The faster you travel, the more I see your clocks slowing down.

This effect, however, is not enough to keep the speed of light constant; there is an analogous effect known as 'length contraction', where lengths increase for observers moving fast (1 meter for me is 1.15 meters for you), but I won't go into that effect today. This idea of time dilation for moving frames of reference has some important consequences:
  • Space and time are not separate entities, they are united. Einstein replaced the notion of space and time, and instead introduced spacetime; two sides of the same coin.
  • Time slows down as we approach the speed of light, so if we reached the speed of light, time would stop completely. You can extrapolate to say that if you move faster than the speed of light; time would move backwards. But nothing can travel faster than the speed of light; as such clocks can't tick backwards. This means that time travel to the past is not possible.
Don't believe me? Check the maths!
Another argument one could naively make is the following. If I'm travelling at 0.6c, and you are travelling at 0.6c in the opposite direction, surely I can argue that you are travelling away from me at 1.2c, therefore you are travelling faster than the speed of light from my frame of reference. This was true from a classical approach, but completely wrong from a relativity approach: you can't just add velocities together like that. When dealing with high speeds, we need to take into consideration time dilation and length contraction. If we take into consideration these effects, you would actually see me moving away at 0.95c, so still within the allowed speed limit.

You might be thinking at this point that we've done everything from my frame of reference. What happens if we change to your frame of reference? Actually, as we've seen that motion is relative, you could argue that you are at rest, and my rocket is moving. In this case, you will see my clocks as running slow. Time dilation caused by motion is also relative: you will see time passing slower for me, and I will see time passing slower for you, which leads us to an interesting paradox.

4. Twin paradox
Imagine we have twin sisters, Elizabeth and Laura. Laura leaves on a round-trip mission to Alpha Centauri, the closest star to the Solar System (except the Sun, of course). This star is 4 light years away (this means it takes light four years to make the journey), and Laura will be travelling at a constant speed of 0.8c. Elizabeth will be staying on Earth, monitoring her sister's journey.
In Earth time, which is the same as Elizabeth's time, the round trip takes 10 years:
$t=\frac{2*d}{v}= \frac{2*4}{0.8}=10$y.
We are interested in how much Laura will have aged from Elizabeth's point of view. We can use the first formula I introduced above to calculate this (or skip the calculation and trust my numbers!):
$t = \frac{t'}{\gamma}= t' \sqrt{1-\frac{v^2}{c^2}} = 10*\sqrt{1-\frac{(0.8c)^2}{c^2}} = 10*0.6 = 6$y
This means that from Elizabeth's point of view, Laura's ship has only felt 6 years, even though Elizabeth felt 10 years. From Elizabeth's view point, when they reunite on Earth, Elizabeth will be 10 years older, while Laura will only be 6 years older.

Now comes the paradox. If we said there are no preferred frames of reference, Laura could argue that she is stationary, and Elizabeth is the one moving. Therefore, from Laura's point of view, she will age 10 years, and Elizabeth will only age 6 years. They can't both be right, so who is correct?

While this result might seem paradoxical, it actually isn't. Laura is naively applying the conditions of special relativity, however we stated above that special relativity works in inertial frames of reference. Laura's ship, however, is not an inertial frame of reference. This is because her ship turns around, and during that time she is changing her velocity. Changing velocity means acceleration, which means it's not an inertial frame.

So how do we study acceleration? Einstein saw that his idea was valid for inertial frames, so he tried to apply it to non-inertial frames. To do that, he needed to think bigger: he needed general relativity. For now, rest assured that the paradox does have a solution: Laura will be younger than Elizabeth after the trip, in the same way that astronauts on the ISS age slower than people on Earth. We'll find out how to deal with acceleration in the next post.

In the second part, we'll discuss general relativity, time dilation from a GR point of view, and we'll revisit the twin paradox, armed with new tools to tackle it better. I'll also discuss some specific examples like the ISS, a possible Mars colony, and of course, everyone's favourite time dilation movie; Interstellar. Be sure to check it out!

Wednesday, 6 April 2016

What's in a theory?

My objective with this blog, apart from having a place where I can ramble about cosmology, is to make science understandable. But if we want to understand each other, we first need to make sure we are speaking the same language, and that often doesn't seem to be the case. I'm not referring to all the scientific jargon that we scientists like to throw around, I'm talking about those words that people use everyday but which have a very different meaning when used in a scientific context. The best example of this is the word theory.

Every time someone misuses the word 'theory',
Schrödinger puts another cat in a box. Maybe.
I'm sure you've seen the situation before: a scientist explains a scientific theory, and someone replies with 'but it's only a theory'. At this point the scientist will cringe, shake their head, and decide it's not worth pursuing the issue. But it is worth pursuing.

The word theory is not a bad word, in fact it's one of the best words we can have in science. Here's the definition:
"Theory (n): A set of statements or principles devised to explain a group of facts or phenomena, especially one that has been repeatedly tested or is widely accepted and can be used to make predictions about natural phenomena." -  Collins English Dictionary – Complete and Unabridged, 12th Edition 2014
Now that we know the definition, let's do some science!
We start with a fact. This is just an observation about the world, that we are very sure is true: it's something we can all observe and agree on. Well, probably all of us; there's always someone who likes to deny the facts ('What do you mean the sky is blue? It looks decidedly green to me'). Let's use an example: I put a coffee cup on the desk, I leave the room for a few minutes, and when I come back the coffee cup is on the floor broken (don't worry; it was empty, no coffee was wasted in this experiment!). Fact: my cup is broken on the floor. So we ask a question: why is my cup on the floor in pieces?

Next we move on to a hypothesis. A hypothesis provides a possible answer to our question regarding the observed fact. We can come up with several different hypotheses to try to answer this question. For our broken cup situation, we could have a few possible answers:

  1. Someone pushed the cup off the table
  2. There was an earthquake/natural phenomena and the cup fell
  3. The table is wonky and things tend to fall off
  4. The cat pushed the cup off the table
  5. The cup thought it was a bird and decided to try to fly.

We use other connected facts to eliminate some of the bad hypotheses. In our example we can use the fact that cups don't think they are birds to discard number five. We can also use the knowledge that there is no one else in the house to discard number one. Number two seems unlikely, as I would have felt the earthquake from the other room. So now we have to do an experiment to test the remaining hypotheses.

For our example, I set another cup in the same place, and I move away to observe. Will the cup fall off because the table is wonky? After several minutes, the cup hasn't fallen. So it seems we can discard the wonky-table-hypothesis. It doesn't take long, however, for a cute cat to jump on the table and knock off the cup, which falls on the strategically placed pillow I set out for our experiment. Maybe we should have left the cat in the box. All the evidence seems to support the fourth hypothesis: the cat pushed the cup off the table. Hypothesis confirmed.

Another very important concept in science are laws. Laws can generally be written as mathematical expressions, and they describe what happens, based on a series of repeated experiments. Newton's law of gravity can tell us how quickly the cup fell off the table. The conservation of mass law tells us that if we add up the masses of all the pieces, we should find the mass of the original cup.

And now we put it all together. We use multiple confirmed hypotheses, based on countless experiments, repeated time and time again, with all the laws describing the experiments, and we group it all together to form a theory. A theory contains laws, confirmed hypotheses and facts, and most importantly, a theory can make predictions about what other facts we can observe. It looks something like this:

And this is how we do science. If a theory makes predictions which don't fit the facts, the theory will be modified. If we find a fact that contradicts the theory, the theory will be modified. Science is constantly changing, and theories are being tested constantly. A theory is the best thing we can have in science, it's telling us 'I am the best model to explain the observed facts, I can make predictions, nothing we have found yet contradicts me, and I have passed every single test you have thrown at me'.

It's not 'just a theory'. It's human beings looking at the universe and saying 'I see what you did there, and I am able to understand it'. And that's awesome.

Still not convinced? Maybe Joe Hanson from It's Okay To Be Smart can help you out:

Friday, 25 March 2016

Cosmology FAQ Part 4 (The End)

As you've probably already heard by now, I recently did a 'Cosmology 101' on Periscope, a two-hour long scope in which I addressed the 25 most common questions in cosmology. Don't worry if you missed it, you can just read these posts.

This is the final part in this series. You can read the previous sections on the Big Bang, the history of the universe, and the present state of the universe. Today we'll answer the big questions.

As always, don't worry if you don't understand everything in this post. This is meant as an overview to give you a general idea of what we do in cosmology. I encourage you to let me know if you see anything mentioned here that you would like to know more about, or that you think is unclear.

19. What is a black hole?
If you throw a tennis ball upwards, you know it's going to fall back down. This is because the gravitational force pulls things together. But if you were able to throw the ball fast enough, it would have enough energy to escape the gravitational pull of the Earth and launch into space. The speed needed to beat the gravitational force of an object is known as the escape velocity. A black hole is an object whose escape velocity is larger than the speed of light. This means that not even light is not travelling fast enough to escape the gravitational force of a black hole. And as we know, nothing can travel faster than light in a vacuum, which means nothing can escape a black hole.

But don't worry; we (probably) aren't going to be swallowed by a black hole. This is because the gravitational force decreases quadratically with distance: if you get ten times further away from an object, the gravitational force is a hundred times weaker. As such, a black hole has an event horizon: an imaginary line that marks the point of no return. If you are further away than the event horizon, you can still escape the black hole's gravitational pull. But you really don't want to cross that horizon: once you do, there's no coming back.

Simulation of a black hole, by Alain Riazuelo
Physically speaking, a black hole is generally formed by the death of a star: when a big enough star reaches the end of its life it can explode as a supernova, leaving behind a really massive - but quite small - object. If two black holes collide, they can form a bigger black hole. 'Normal-sized' black holes are generally between 5 and 35 times the mass of the Sun. And then we have their older brothers: the supermassive black holes, which can be million times more massive than the Sun, and play a really important (but not fully understood) role in the formation of galaxies.

Mathematically speaking, black holes are regions where the curvature of spacetime becomes infinite (Einstein taught us that this curvature is what causes the gravitational force). These regions are known as gravitational singularities, which leads to an important question...

20. Was the Big Bang a Black Hole?
You've heard me before describe the Big Bang as a singularity, and I've just described a black hole as a singularity, so it is logical to ask if they are the same thing. But actually, the Big Bang was nothing like a black hole. The main difference here is we believe the Big Bang was a singularity, with time and space existing inside the singularity. So the Big Bang was a singularity of space and time, whereas a black hole is a singularity in space time.

21. Is our universe unique? What is the multiverse?
There are many different theories in physics that support the existence of multiple universe. Some people claim there are an infinite number of universes, each with different laws of physics, and we just so happen to live in the region which has the conditions necessary for us. Other people claim that when the universe inflated, it did so in little 'pockets' with each pocket universe evolving with a different amount of inflation, leading to very different universes. In any case, we have no way of accessing these postulated alternative universes, or obtaining any information from them. Therefore, it is not a productive question: it deals with something we don't know nor have any ability to know, and that is not likely to change soon. It is an interesting thought exercise, but it's not really a useful question from a scientific point of view.

22. What is dark matter?
This is one of the biggest open questions in physics. We are fairly sure that 25% of the universe is made up of dark matter, but we don't yet fully understand the nature of this mysterious matter. It's a type of matter that doesn't interact with the electromagnetic force; this means it doesn't emit, absorb, or reflect light, so we call it 'dark'. We are also quite sure it doesn't interact via the strong force, which means it doesn't form big clumps: the dark matter particles don't bind together. It does, however, interact via the gravitational force. And this is how we know of its existence.
There are several main evidences for the existence of matter we can't see. One such example is the rotation curves of galaxies. In a normal galaxy, we would expect the stars further away from the central bulge to move slower; in the same way that Neptune moves around the Sun slower than the Earth does. However, when we take enough measurements of galaxies, we actually see that the outer stars are moving at the same speed as some of the closer stars. The following plot shows the velocity (vertical axis) and distance (horizontal axis) of the stars in a galaxy.

The only way we can explain this with our current laws of physics is by assuming there is more mass located in the halo of the galaxy: a huge amount of matter that we can't see.
Other evidences for dark matter include merging of galaxies, and weak lensing, which I'll elaborate on in a future post, but the idea is the same: if our theories of gravity are correct, the visible matter in the universe is not enough to explain the observed phenomena. There are hundreds of experiments currently trying to find what we have not yet been able to see.

23. But what if we are wrong about gravity and DM is not real (MOND)?
There are some physicists who believe that instead of assuming dark matter is real, we should assume our laws of gravity are wrong. There are some who argue that instead of looking for 'invisible' matter, we should instead modify our theories of gravity (MOND). While these models are able to make some predictions, they can't explain observations we have made in galaxy clusters, nor can these models be used (yet) to build a complete cosmological model. They have often been described as being 'ad-hoc', with more elements added to an ever-complicated model to try to fit the evidence. These models have lost favour in recent years, but some people still pursue them.

24. How will the universe end?
There was recently a great review about this topic on the BBC. There are several different possibilities as to how the universe might end, although the data seem to favour the first two.
  • Big freeze/heat death. The expansion of the universe is currently accelerating. If this carries on, the universe could expand forever. This means everything would gradually grow further and further apart, while cooling down and approaching absolute zero. Entropy would reach its maximum, which means there would be no exchange of information nor exchange of heat. Everything would just freeze. In this scenario the universe ends up very cold, dead, and empty.
  • Big rip. If the acceleration of the universe increases, perhaps caused by an even stronger type of dark energy, the rate of acceleration could increase so much that it could overcome the pull of gravity on ever smaller scales. As a result, all material objects in the universe, starting with galaxies and eventually all forms of mass, no matter how small, will be ripped apart; reverting back to unbounded elementary particles and radiation, shooting away from each other.
  • Big Crunch. This is a very nice, philosophical view of the universe. In this scenario the universe is cyclic; it begins with a Big Bang, pushing everything outwards. At some point, this expansion will stop and go the other way; collapsing back inwards, causing everything to crash together until a singularity is formed - which would then be the singularity for a new Big Bang, a new universe. Like a phoenix rising from the ashes of an older universe. This is a scenario that many people like, unfortunately the universe doesn't care what we like: the current accelerated expansion of the universe seems to disfavour this model. 
  • False vacuum. A lot of things in the universe like to be in their 'least energetic state': the configuration that needs less energy. This is known as minimum potential energy principle, and it affects diverse things like electrons in an atom, atoms in a crystal, a marble in a bowl, and those lazy Sunday mornings when we just want to stay in bed and not spend any energy. Going back to the idea of the multiverse, if our universe is just one among billions of expanding bubbles, we could imagine that there are universes out there at a lower energetic state than ours. This would mean our universe is in a 'false vacuum': a local minimum of energy, but not a global one. If our universe came close to one of these other pocket universes, we could 'collapse' to their lower energy level. Imagine if you are heading to the gym but your friends are planning to spend the day sunbathing on a beach. It's quite likely that you would skip your gym plans and adopt their plan of 'least energy'. We can't really fault the universe for doing the same. If this happened, it could fundamentally alter our universe by changing some constants of nature, or even the very nature of space and time. Structures could be destroyed instantaneously, without any forewarning. As scary as that may seem, by studying the particles in our universe physicists believe this couldn't happen for at least a couple of billions of years.
In any case, the Sun will expand in four or five billion years and probably destroy the Earth in the process, so it's unlikely we'll be around for the end of the universe.

But don't worry, we live in a universe with puppies, chocolate, and coffee, so we don't need to concern ourselves with something so many years into the future.

25. How can I become a cosmologist? What good books do you recommend to get me started?
There is still so much we don't know about the universe; we can only see 5% of it, and we probably understand much less. Cosmology is a really active field, with a lot of discoveries waiting for us. If you are considering a career in cosmology, I strongly recommend it. To become a cosmologist first you need a Bachelor/undergrad in Physics, and take as many maths courses as possible. Follow up with a postgraduate in Astrophysics or Cosmology: some countries allow you to directly do a PhD, others require you to first do a Master's. In either case, the postgraduate studies will take about 5-6 years. All in all, to become a Doctor of Physics, you need about 9-10 years of study. It is worth it.
Also, go to as many seminars as possible, try to read scientific articles, and don't be afraid to email the authors if you don't understand things: they are generally happy to discuss their work!

If you want to get involved without all the studying, there are plenty of citizen science projects you can help out with.

Finally, if you want some good books on the topic, check out this list. If you know of any books I forgot to include in the list, let me know!

We did it! We got through the 25 most common questions in cosmology. I will elaborate on most of these topics in the future, but for now we have a good starting point.

Saturday, 12 March 2016

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.