This is the sixth part of the VERITAS series on General Relativity. Just to remind our readers: We are doing this series on Einstein’s Theory of Relativity to celebrate the 100th Anniversary of General Theory of Relativity. If you have missed any of the first five parts, you can read them here:
In the previous parts we have studied the basic ideas behind special and general relativity. We have discussed how gravity bends space time and slows down time. We have also explored one of the most interesting and astonishing results of relativity: black holes. If you have not read the previous parts, I suggest you read them before reading this one.
In this article we will apply General Relativity to the biggest possible problem that can be thought of: the whole universe. We will understand the current theory of how the universe originated and how it evolved after that. We will also see how the universe will evolve into the future. We will also learn about dark energy and dark matter. But before we move further, think about the magnitude of what modern physics allows us to do: we, tiny creatures living on a small planet revolving around a small star in one corner of a medium sized galaxy( which contains over 100 billion stars) have developed the ability to ask and try to answer questions about the whole universe which contains billions of galaxies like our own!
Our view of how big the universe is and what our place in the universe is has evolved over time. For most of history we have thought that the universe is small and we are its centre- a special world that God has created and continues to administer on a day to day basis J. In the 16th century Copernicus placed Sun at the center of the universe. This was a big change in the human view of the universe and our place in it. Of course, religious authorities were disgusted at this idea- you see Religion is not so much about the importance of God, it is more about the importance of man in a universe that God has specifically created for him. Copernicus’ model placed sun at the center of the universe but the actual extent of the universe was not known. It was only in the 1920s that the first galaxy outside our own( Andromeda) was identified- it was referred to as an “island universe”. This was another big change as now, the milky way was not the only galaxy. Suddenly the universe was much much bigger than what we had imagined. Since the time of Copernicus and Galileo, the size of the earth relative to the universe and its importance in the grand scheme of things has kept steadily decreasing. And then in the 1930s the human “ego” suffered another blow- not only is Earth an insignificant planet, the universe is expanding and thus increasing our insignificance enormously with the passage of every moment . The universe is getting bigger! Edwin Hubble had examined the relationship between the distance to galaxies beyond the milky way and “red shift” in the light received from them and had come to this conclusion.
The universe is expanding. In whatever direction you look, galaxies are receding away from us. Now this does not mean that we are the cente of the universe. Think of a cake with raisins in it. When the cake is being baked, it expands. The raisins seem to move away from each other. If you were on one of the raisins, you will see all raisins move away from you. It does not matter which raisin you are on, you will see the same thing. This is similar to our universe. No matter which galaxy you are on, all galaxies in all directions seem to move away from you. So, there is no center of the universe. Also, if the size of the cake doubles, the distance between the raisins doubles. So if at one particular time the distance between your raisin and the neighboring one is 10 cm, it will become 20cm when the cake doubles. Now imagine a raisin 20 cm away from you. When the cake doubles, the raisin’s distance from you becomes 40 cm. So we see that the raisins that are further away from us appear to move away faster than the ones that are closer. This is similar to the universe. The galaxies that are far away from us appear to move away at a faster rate. The relationship between distance of a galaxy and the velocity at which it appears to move away is called Hubble’s law. It is v = H X r. r is the distance, v is the velocity of the galaxy going away from you. H is the Hubble constant. The Hubble’s law can be derived from the General Theory of Relativity.
In 1927, Georges Lemaître proposed the idea that if all galaxies are moving away from each other, there would a time in the past when they would all be at the same place. So, at some distant time in the past, the entire mass of the universe was concentrated at a single point. And then an event known as the Big Bang occurred and that caused the universe to come into existence. The universe has been expanding ever since. The Big Bang is a consequence of Einstein’s theory of relativity applied to the entire universe. How does one apply a theory like relativity to the whole universe? Physicists first make a model of the universe and then apply the equations of relativity to it to see how the universe would have been earlier and what may happen to it as time passes. The simplest possible model of the universe is that of a fluid with a positive mass density but no pressure. Such models are called dust models( see Wikipedia: https://en.wikipedia.org/wiki/Dust_solution). One of the most interesting and important examples of the dust model is the Friedmann–Lemaître–Robertson–Walker model. This describes a universe that is isotropic and homogenous. By isotropic we mean that no matter where you go in the universe, you will see similar stuff around you. So on a large scale the universe in terms of matter density and radiation is the same everywhere. By homogenous we mean that in whichever direction you look you will see similar stuff. So if I look towards west, the galaxies are moving away from me according to Hubble’s law. The same will be true even if I look toward the right or towards any direction. So by isotropy and homegeniety we mean that the universe is the same( on a large scale) at every place and thus has no preferred place( no centre, of course) and no preferred direction. Once we have a model of the universe we can then apply Relativity to the model of the universe and come up with solutions as to its past and its future.
The following Wikipedia image shows how the universe evolved according to our current understanding:
So, the universe began about 13.7 billion years ago. The most interesting part of this evolution is just after the big bang. The universe expanded 10^26 times in a fraction of a second! This period is known as cosmic inflation. After that initial period of superexpansion, the universe settled into a slow regular expansion that has continued to this time. The first stars were formed about 400 million years after the big bang. The development of galaxies happened much later. Our own milky way is 9 billion years old and the sun is about 5 billion years old. Note that during the time of inflation, the universe expanded at a much faster rate than the speed of light. This does not violate Einstein’s relativity. Nothing in the universe can travel faster than light but the universe itself can expand faster than the speed of light. If you look at the far right of the above figure, you can see that the universe seems to be expanding at an accelerated rate. Not only is the universe expanding, the expansion is accelerating. This fact was discovered very recently – in 1998. We will have more to say about this later.
Now, the above image shows what has happened till now. How will the universe evolve in the future? In the earlier versions of this series we learnt that gravity is actually a distortion in space-time. It would be natural to think that the universe may also have a shape that is determined by the sum total of its gravity. The shape of universe thus determines the total amount of gravitational energy in it and that ultimately determines its fate. See the following image from Wikipedia:
The omega in the above image is known as the density parameter. If it is greater than 1, the universe is said to be closed. In that case, the universe may not expand forever. It will stop expanding and then start contracting into a tiny lump of matter with “infinite” density. This scenario is called the big crunch. If the universe’s density parameter is > 1 the universe will continue to expand forever at an accelerated rate. In that case the universe will be “torn apart” due to huge expansion called the big rip. The third scenario is known as the big freeze- the universe will keep expanding at a slower rate and ultimately each particle would be far away from any other particle in the universe- it would be a uninteresting universe without any stars or galaxies: just a cold, dark, lifeless universe.
Can we determine the density parameter of the universe and determine which of the three possibilities, big rip, big crunch and big freeze will happen? We cannot determine the exact value of density parameter because of two big unknowns- dark energy and dark matter. When scientists compared the estimated mass of galaxies by summing the masses of stars to how the gravitational field changes as we move outwards from the centre of the galaxy, they observed something strange. There was more mass in the galaxy than could be accounted for by the sum of the masses of all the stars. They called this unknown and unseen matter, dark matter. Astonishingly, they calculated that there is more dark matter than “normal” matter in the galaxy. Now lets talk about Dark Energy. I have stated earlier that the universe’s expansion is accelerating. Why should the universe accelerate while exapanding? All the gravity in the universe should pull it inside. What is the force that is making the universe accelerate by countering gravity that is trying to stop the expansion? The force is still a mystery. Scientists have theorized that there may be energy of a different kind that is causing this accelerated expansion. They call it Dark Energy. Note that according to Quantum Mechanics, even vacuum has some energy called zero point energy. Some scientists think that zero point enegy may be dark energy. However the exact nature of dark energy is not known.
The ultimate fate of the universe depends on the amount of dark energy and dark matter in the universe and the physics of these mysterious forms of matter/energy. The current estimate is that 68% of the universe is dark energy, 27% is dark matter and only 5 % is “normal” matter that we see around us( normal matter is the matter that makes up the visible stars, planets, galaxies etc). So it is safe to say that we have no idea about 95% of the matter/energy in the universe. Dark energy and Dark matter are some of the biggest mysteries in physics.
Another question that gets asked is: what happened before Big Bang? In the previous VERITAS article we studied that every Black Hole has at its centre a place that we call the singularity. A singularity is a place with infinite density and it is a place where the laws of physics break down. The Big Bang was also a singularity. So we cannot know about the Big Bang or what happened before it using our current understanding of physics. We can only use physics to understand what happened after the Big Bang.
Isn’t it amazing that Einstein’s theory of relativity, which he composed while sitting on a desk can be used to understand the whole universe. As Einstein said “The most incomprehensible thing about the universe is that it is comprehensible”
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Go wondrous creature, mount where science guides
go measure earth, weigh air, state the tides,
instruct the planets in what orbs to run
correct old time, regulate the sun
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