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An outline of the evolution of the universe, from the big bang to the eventual heat death
Email : davidn@dfdn.info
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Just a note: in this article, we are dealing with both extremely small and extremely large periods of time! As it is not easy to type exponents on a keyboard (!), I use ^ to indicate 'ten raised to the power of'. So for example, 10^3 years is 100 years, and 10^6 is 1000000 years. We have to deal with powers of ten from 10^-43 to in excess of 10^100 years, the latter is 1 followed by 100 zeros - a googleplex! There is no physical number like this in existance! Attempts to visualise this number are soon thwarted! For example, the number of stars in the known universe is around 10^23 and the number of protons calculated to exist in the observable universe is 'only' around 10^78!
1: The Primordial Era
The first age of the universe is what we call the Primordial Era, which is really the Big Bang Theory. In the beginning, there was no real space or time, because space and time had not yet separated. Also, in this Primordial Age, quantum theory and general relativity have to be incorporated in a theory ofquantum gravity to describe the universe. At this moment, the universe is roughly 10^ to-the-minus 43 (10^-43) seconds old, and out of this quantum gravity epoch, some type of nucleation event leads to the production of our universe. What this means in practice is that some small region of space-time bursts into existence, and "into existence"means, in this context, that space and time became defined in that tiny region. From that moment onward, our universe, as a universe, exists, and it is the goal and job of cosmologists to how that evolves. Here’s the story..
The first thing that happens in the universe's existence is that it starts inflating incredibly rapidly. This early phase of extremely fast expansion explains many of the properties that we see in our universe today, such as why it’s homogeneous and isotropic (in other words, why the universe is the same everywhere in space and why it looks the same in all directions that we look in the sky). This early burst of rapid expansion also explains why the universe is as old and as flat as it is. .
This inflationary stage occurs when the universe is about 10^-37 seconds old. In the early stages of the universe, everything is in the form of radiation. Particles and anti-particles come in and out of existence on a regular basis. Between that time and the one-microsecond mark, perhaps the most important event in the early universe happens. Matter is created. Now, most of the laws of physics are symmetric with respect to matter and anti-matter. And the physics experiments that we've done so far support the theory that when you create matter, you also create an equal amount of anti-matter (that can annihilate with matter). But we don't live in an anti-matter world. If you touch the person next to you, you don't explode. When we landed people on the moon, the astronauts didn't explode in a matter-anti-matter reaction. What that means is that everything in this room or on the moon is made of matter and not anti-matter. Through more indirect methods, astronomers have successfully done this experiment across the universe, almost all the way to our cosmological horizon today. In that whole volume, as best we know, all material is made of regular matter and not anti-matter. This is very important. What this means is that during the first microsecond of cosmic history, some process set up an asymmetry between matter and anti-matter, producing a little bit of extra matter..
The amount of excess matter that was produced in the earliest existence of the universe was tiny. If you had 30 million anti-matter quarks, it would annihilate 30 million matter quarks, with one quark left over made of regular matter. That one extra matter quark in 30 million is just like a contaminatung residue, but that’s the only thing that survives the early universe to become everything that you would call ordinary matter in our universe today. After the microsecond mark, those excess quarks condense and make protons and neutrons for the first time..
This event has profound implications for the future of the universe. Namely, if there is a process that can prefer matter over anti-matter, or the other way around, such a physical process is still around. If we know that there's a process that can be asymmetric with respect to matter and anti-matter, then every proton in the universe is eventually doomed. We think that protons live longer than 10^33 years, but somehow, some way, in the far future all of the protons will decay. So matter is not forever. It lives from the microsecond mark in the universe, and it only lives until protons decay, sometime later in our story. .
By the time the universe is one second old, it has cooled enough that protons and neutrons can get together and form large nuclei like helium. The amount of helium that is produced in this early burst of nucleosynthesis--that starts when the universe is a second old and ends when the universe is about three minutes old--is the vast majority of all the helium in our universe. Stars produce helium today, but this early burst of nucleosynthesis generated more helium than all the stars that have ever lived anywhere in our universe. Similarly, this early interaction produced more energy than has been generated by all the stars in the universe today. This is an enormously energetic event. It is the smoking gun of Big Bang Theory. Without this theory, there's no other way to account for the helium that we see today in our universe. .
We also feel that the Big Bang Theory is on solid footing because if the universe did go through such an early hot dense phase, there should be some residual radiation left over, which can be called the afterglow of the "Big Bang." And we can see this radiation in the sky. The whole universe is filled with a pervasive sea of microwaves. In fact, the universe is similar to a really low-power microwave oven. What's more, if the universe were hot and dense in its earliest phases, then the distribution of the energy in this background should have a certain blackbody shape. This shape indicates that there's almost no way that this radiation could come from anything other than an early, hot, dense "big bang." What's more, although the universe is very homogeneous in that the temperature in this microwave background is the same everywhere in the sky, it's not quite the same. It's only the same to one part in a hundred thousand. And this departure of one part in a hundred thousand is very significant. First of all, it's a heroic effort to measure; it wasn't measured until the very early 1990s. Most importantly, these small fluctuations eventually form the galaxies. They condense through gravitational contraction, and eventually condense into galaxies, clusters of galaxies and larger-scale structures..
2: The Stelliferous Era
The Primordial Era ends when the universe is about a million (10^6) years old and generates its first stars. We then enter into the current era, called the Stelliferous Era, which extends from cosmological decade six to about fourteen (10^6-10^14), ending when the universe is about 100 trillion years old. .
The Cosmological Decade:.
As we move into vast expanses of future time, I'm going to introduce a logarithmic time unit, called the cosmological decade. So if I write the time in years as 10^ to some power (e.g. 10^5), which is 100,000 years, the exponent is called the cosmological decade. Keep in mind that the universe is now 10 billion (10^10) years old, so we're now living in the tenth cosmological decade. When the universe is 10^ times older than it is now, the universe will be 10^11, and we'll be in the eleventh cosmological decade. We'll talk about the history of the universe up to a hundred cosmological decades. Remember that this kind of "decade" does not last a set amount of time; the tenth cosmological decade takes 10^ times as long as the ninth cosmological decade took, and the eleventh cosmological decade will take 10 times longer than the tenth, or 100 times longer than the ninth..
Right now, stars are the most important objects in the universe, in a sense, because the stars are the source of most of the energy that is generated in our universe today. The sun is a star, and the number of stars in the universe is about the same as the number of sand grains in a big sand dune, about 10^23 if you want to put a number on it. Most energy in the Stelliferous Era is generated through the process of nuclear fusion--the fusion of hydrogen into helium--which releases energy. This process powers the sun now and will continue to do so for about 7 billion years. At that time, the sun will turn into a red giant, with its outer surface expanding from its current small position to about the radius of the Earth's orbit. Now, you don't have to worry about that event 7 billion years from now, because long before, in about 3.5 billion years, life on Earth will already be gone. As the sun gets older, it gets brighter, heating the Earth, creating a catastrophic, runaway greenhouse effect that will make global warming seem like a walk in the park. It will boil the oceans and completely scald the entire biosphere. .
You might have heard that our sun is an ordinary star. Well, you've been lied to. If you look at the 50 nearest stars, the sun is actually the fourth largest. The typical star has a mass about a quarter of that of our sun. If you look at the population of stars in the galaxy as a whole, most stars are actually smaller-mass stars. These red dwarfs live much longer than our sun, typically trillions of years. The smallest star that can burn hydrogen is about 8 percent of the sun's mass and about a thousand times dimmer. When it dies, a star like the sun becomes a red giant, growing about a hundred thousand times brighter than its current luminosity. But these little stars never become red giants; they just stay at about the same small size, then turn around and become white dwarfs when they die..
Let's take an inventory of the stellar population of the universe. About half of the stellar bodies are brown dwarfs, which are failed stars. They are objects with a mass of less than about 8 percent of the sun and are too small to sustain hydrogen burning. Brown dwarfs sit around for trillions of years and do essentially nothing. That's very important in the future because all of the accessible unburned hydrogen in the universe will be wrapped up in these brown dwarfs. Half the stars that exist really are stars in the sense that they burn their hydrogen into helium. The vast majority of these are red dwarfs, stars much smaller than the sun. There are a small number of sun-like stars, and an even smaller number of massive stars that burn themselves out more rapidly. .
We can determine how long stars continue to burn to burn their hydrogen into helium. Most of the stars that are hydrogen-burning stars (every star from about 8 percent of the solar mass all the way up to eight solar masses, which is 997 out of 1000 stars) become white dwarfs when they die. Our sun will do this after its red giant phase. The sun will shed about half of its mass, and the core at its middle will shrink to about the size of our Earth. This future sun will have a density about a million times denser than the current sun, and it will be a degenerately supported object called the white dwarf. A red dwarf star also becomes a white dwarf but preserves most of its mass. Becoming a white dwarf is the fate of the vast majority of all hydrogen-burning stars..
About three out of a thousand true stars have a more dramatic end in store for them. At the end of their lifetimes, they blow up in a supernova explosion. When a super nova explodes, two possible things are left behind--a neutron star and a black hole. A neutron star is what you get when you take something the mass of the sun and compress it down to about the size of Bristol, about 10 kilometers in radius. It's almost one big atomic nucleus, and that object is supported by the degeneracy pressure of its neutrons. If you then take that object and compress it another three or four times smaller in terms of radius, it will become a black hole..
When you take all of the relevant processes into account, the longest that a galaxy like our Milky Way can sustain star formation is about 10 trillion years, close to the lifetime of the longest-lived star. This tells you that the universe will undergo a fairly sharp transition between a universe with stars and a universe without stars. During the thirteenth cosmological decade (10^13 years), when the universe is 10 trillion years old, the stars will still be shining brightly. Because the stars get brighter as they get older, the galaxy won't be much dimmer than it is today even though most of the stars will be small stars. But when the universe is 10^ times older, in the fourteenth cosmological decade (10^14 years), all of the stars will have burned out, or exhausted their hydrogen. The galaxy will have run out of gas to make new stars, so the process of star formation will also shut down..
3: The Degenerate Era
When stellar evolution comes to an end, we enter the Degenerate Era. Most ordinary stars will be done with the business of nucleosynthesis as stellar bodies. In our inventory of stars, we have about equal numbers of brown dwarfs and white dwarfs, and about three in a thousand black holes and neutron stars. Since the white dwarfs are quite a bit larger than the brown dwarfs (by about a factor of 10 in mass), the vast majority of the actual (baryonic) mass--the protons--are embedded in these white dwarfs. Although a lot of gas is also left behind in this future universe, it's very diffuse and wispy. In sum, what are left in the Degenerate Era are degenerate stellar remnants (degenerate here refers to a quantum mechanical property of dense matter, not to a moral statement about the universe). From cosmological decade 15 to perhaps 37 (10^15-10^37 years), these degenerate objects are the most important stellar objects in the universe. .
At this point the brown dwarfs--the failed stars--start to come into play because they can collide. In our universe today, astronomers never worry about stars colliding, and the reason is simple. The amount of space that is filled by stars is phenomenally small. Populating the universe with stars is like taking little tiny sand grains and putting them miles and miles apart. With that much space between the stars, collision is very rare..
However, if you wait long enough, sometimes things that are unlikely do, in fact, happen. And if you wait long enough, stars are going to collide in our galaxy. When two brown dwarfs collide at a sufficiently head-on angle, then the merged product can have enough mass to sustain hydrogen fusion. The result is a star with enough mass to turn on and become a red dwarf just over the hydrogen-burning limit. It will then burn up the hydrogen it has previously hoarded. This star won't be large like our sun; it will be another one of these typical little red stars that lives for trillions of years..
Since we know how many brown dwarfs there are, and we know the galaxy they live in, and we know the collision rate of these stars, and we know how long the merged products will live, you can add all these things up and calculate how many such stars should be shining in a large galaxy like our Milky Way at any given time in the Degenerate Era. And the answer is two or three such stars. Today, as Carl Sagan has told us, there are billions and billions of stars in every galaxy, and they are bright. In this dark galaxy of the future Degenerate Era, there will be two or three stars from these merged brown dwarfs, and they will be about 10000 times dimmer than the sun. Every once in a while the white dwarfs will also collide. But most white dwarfs are small, so when they collide they will just form weird stars and will not do anything interesting. .
But, occasionally, when the big white dwarfs collide, the merged product can be large and fat enough that it will explode in a different kind of super nova explosion. So every once in a while this dark galaxy of the future will be punctuated by a spectacular super nova. .
White dwarfs also sweep up dark matter particles. Over time, inside the white dwarf, these particles annihilate each other, turn into radiation, and become the dominant energy source in the universe. The power generated by such a white dwarf is about quadrillion watts, which is quite small compared to the sun, but that's a healthy fraction of the energy that our earth intercepts from the sun. Over longer times, the galaxy itself changes its structure by evaporating its stars out into the intergalactic void. We would have a continual hierarchy of these dynamic processes, but protons will eventually decay. For illustration here, let's say that 37 cosmological decades (10^37 years) is the typical proton lifetime. Most of the protons that we care about at this late stage in history will be embedded in white dwarfs, which is a very dense medium. Not only will there be protons, but also there will be the corresponding electrons around. When a proton decays into a positron, this positron will very quickly find an electron to annihilate with. The net result of a proton decay event inside a white dwarf star is thus to turn all of the mass energy into radiation. In particular, you get four photons. Those photons then interact with the other things in the star and transform into more and more low-energy photons as the energy works its way out of the stellar surface. The star surrenders its mass in the process..
With that picture in place, we can know, for the first time, the complete evolution of the sun, which will become a red giant and then a white dwarf once it cools and becomes smaller. In the long run, the proton decay process is the most important mechanism driving stellar structure. As the white dwarf radiates its mass and energy away, it grows larger even as it loses mass because degenerate objects work backwards. A white dwarf star undergoing proton decay will generate something like 400 watts of power--about as much as you can do on a rowing machine if you're working pretty hard. This process of degeneration will continue until the mass of the object has decreased from about the mass of the sun down to something close to the mass of Jupiter. At that point the object loses its degenerate properties, but the protons keep decaying. The star is now much like a block of hydrogen ice, with a dwindling store of mass and internal radiation escaping out of the body. Eventually, the block of hydrogen ice no longer exists and stellar evolution comes to an end. That is the long-term fate of our sun, and most other stars. .
We began the Degenerate Era with an inventory of brown dwarfs, white dwarfs, neutron stars and black holes. We've seen that stars continue to form through these brown dwarf collisions. Dark matter gets captured in white dwarfs and endows the white dwarfs with a luminosity source, a power source that they wouldn't otherwise have. Against this backdrop, the galaxy rearranges its structure over time scales of 10^20 years or so, relaxes dynamically, and evaporates most of its stars out into intergalactic space. All the while, black holes that capture stars and gas and anything that they can get into their event horizons grow somewhat larger during this time. The Degenerate Era ends rather cleanly after the protons decay. For the numbers we're using here, this era ends after 10^40 years, or cosmological decade 40. .
4: The Black Hole Era
The only objects that survive unscathed through that epoch of proton decay will be black holes. Black holes may or may not be composed of protons, but the beauty of black holes is that you cannot even really see whether they’re made of protons or not. As we leave behind the Degenerate Era, we enter into the fourth era, called the Black Hole Era. Black holes are objects that are so dense and so massive that their escape velocity is greater than the speed of light. The original definition of a black hole is that nothing can escape its surface because it would require a speed faster than light..
And that would be true if it weren't for quantum mechanics. Stephen Hawking realised that if you add quantum mechanics to our understanding of a black hole, then it is possible for radiation to leak out every once in a while. The process is so slow that you don't need to worry about this today. But in the future, when all of the other stellar objects are gone, black holes shining through this Hawking radiation are the brightest objects in the universe. They will fill the role now played by stars in our universe today..
Before we actually talk about the implications of Hawking radiation, let me justify to you that black holes can exist. One way to create a black hole is through a super nova. When the most massive stars explode at the end of their lifetimes, they do so in a super nova explosion. Left behind is either a neutron star, which is a very dense remnant, or a black hole. If a neutron star remnant gets too massive, and here massive means more than about twice the mass of the sun, the object will collapse to a black hole..
We now have observational evidence that these stellar-sized black holes exist. It is hard to project exactly how many there will be in this universe of the future, but there should be about a million such black holes in a galaxy the size of our Milky Way..
There's another kind of black hole that we also "see." The middle of every galaxy has a super-massive black hole. Not surprisingly, a supermassive black hole means one that has a lot of mass, but here, "a lot of mass" means millions to billions times the mass of the sun. Our own galaxy has a rather modest such specimen containing about 3 million solar masses of material. The central black hole of other galaxies can be up to billions of solar masses. If you look at the central region of a galaxy and watch how fast the stars are moving around the very centre, you find that the stars are orbiting very quickly around something that you can’t see. That something you can't see is compressed to an extraordinarily tiny volume. About the only thing it can be is a black hole, and the mass of these black holes is large. If you do an inventory of the universe in the Black Hole Era, you will only find black holes. Each galaxy that is about the size of ours contributes about one super-massive black hole and about a million stellar black holes to this inventory. And each black hole is shining brightly, or as bright as it can be, through Hawking radiation..
But black holes have their own lifetime, which depends very sensitively on their mass. Not only do the bigger black holes have more mass to radiate away, but they also radiate that mass away at a lower temperature. So the super-massive black holes live much longer than stellar black holes. The numbers work out so that if you have a one solar mass black hole, a black hole with the mass of the sun, it will live for 65 cosmological decades (10^65 years). The typical stellar black hole that is produced by a super nova explosion is expected to be about 10 solar masses. This kind of black hole would live a thousand times longer, or about 68 cosmological decades (10^68 years). A million-solar mass-black hole--like the one that lives in the middle of our galaxy--would live for 83 cosmological decades (10^83 years). The largest black holes you can envision would swallow nearly the whole mass of a galaxy, but even such an enormous black hole as that would radiate itself away in only 98 cosmological decades (10^98 years). And finally, if you took every bit of mass in our observable universe today, and you balled that up into a tremendously massive black hole, that object, too, would radiate itself away in only 131 cosmological decades (10^131 years). That is a very long time, but compared to forever, it’s really quite short. Eventually, black holes are going to make their explosive exits from the universe, and we will enter a new era--the fifth and final era, called the Dark Era. .
5: The Dark Era
As we go this far into the future, our powers of prediction begin to lose focus. One thing we can say is that all the processes that we have talked about so far leave behind backgrounds of radiation. As we saw, red dwarfs continually pump radiation into the universe during the Stelliferous Era, and the stellar background light will overwhelm the microwave background light. So the stellar contribution to the radiation fields will rise, but only until the time when stars die. At that point, that radiation will decay in prominence. In the Degenerate Era, the dark matter annihilation in white dwarfs then becomes the most important process, followed by the proton decay process that produces the most important source of radiation. Finally, the black hole radiation process--Hawking radiation-- becomes the most important radiation background in the universe. That brings us to the beginning of the Dark Era, where we have no more stellar bodies, only an inventory of leftover particles: positrons, electrons, neutrinos and lots of long-wavelength photons..
What is surprising about the Dark Era is that the universe is not dead yet, and interesting things still continue to happen. For example, protons often leave behind positrons when they're gone, so for every electron that is still around in this dark future, there will be a corresponding positron. Electrons and positrons can get together and form what’s called a positronium atom, which is like a hydrogen atom but where the positron plays the role of the proton. We can make these positronium atoms today, but they are microscopic. They live for a tiny fraction of a second and then annihilate when the electron and the positron converge. In this far future, if you form a positronium atom, it will be bigger than our galaxy in size. It can be even as big as the whole universe today in size. The universe is so empty that these things can live as tremendously large atoms, and the electron and positron will circle around each other for perhaps 145 cosmological decades (10^145 years) while they cascade down through various energy levels until they annihilate, emitting very long wavelength photons as they go..
There are other possibilities. One of the possibilities is that we now live in a universe that has a non-zero cosmological constant. A recent set of experiments, done in the last couple years, suggests that our universe may be accelerating. If this is true, everything just explained still holds. But it also opens up another possibility, namely that our universe lives in a false vacuum. In order for the universe to accelerate, empty space needs to have an energy level. But as soon as you allow the universe to have a vacuum with an energy level, then automatically the universe is theoretically allowed to have two energy levels. There is the possibility that a lower energy level exists, which means there is a possibility that a transition can occur, from the high energy state of today to a low-energy state of tomorrow. What's surprising is that, if you knew the theory, you could actually calculate the time scale over which this happens. However, the theory and the parameters are unknown, and the result is extremely sensitive to the unknown parameters..
But if such a thing is happening or does happen in the future, what you get is something like this: A nucleation picture in which tiny regions make a transition from the old vacuum state to the new vacuum state. These regions grow with time, eventually percolate and merge, and transform the whole universe into a new phase. If the universe undergoes such a phase transition, then the transformation can actually change the laws of physics. Because the strength of the forces and the masses of the particles can be wrapped up in the properties of this phase transition, the properties of physics can be different before and after the phase transition. Even though this dead universe, 10^100+ years old, has essentially done all it is going to do, there is a chance for a new start..
Now, we're really starting to get a little bit speculative, so what I want to do is bring us back to earth and remind you of two things. One, that as the universe continues to age, it goes through a whole host of interesting processes which last from now until the universe is at least 100 cosmological decades (10^100 years) old. Second, with this grander perspective, we can now look back to where we are now. Although we don't occupy a particularly important place in space or a particularly important place in time, in cosmic terms, we actually do occupy a pretty good planet for the qualities that we have. We are pretty lucky to be here on Earth.