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heusdens
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Inflation for beginners [part 2]
The reason why the GUTs created such a sensation when they were applied to cosmology is that they predict the existence of exactly the right kind of mechanisms to do this trick. They are called scalar fields, and they are associated with the splitting apart of the original grand unified force into the fundamental forces we know today, as the Universe began to expand and cool. Gravity itself would have split off at the Planck time, 10-43 of a second, and the strong nuclear force by about 10(exp-35) of a second. Within about 10-32 of a second, the scalar fields would have done their work, doubling the size of the Universe at least once every 10-34 of a second (some versions of inflation suggest even more rapid expansion than this).
This may sound modest, but it would mean that in 1032 of a second there were 100 doublings. This rapid expansion is enough to take a quantum fluctuation 1020 times smaller than a proton and inflate it to a sphere about 10 cm across in about 15 x 1033 seconds. At that point, the scalar field has done its work of kick-starting the Universe, and is settling down, giving up its energy and leaving a hot fireball expanding so rapidly that even though gravity can now begin to do its work of pulling everything back into a Big Crunch it will take hundreds of billions of years to first halt the expansion and then reverse it.
Curiously, this kind of exponential expansion of spacetime is exactly described by one of the first cosmological models developed using the general theory of relativity, by Willem de Sitter in 1917. For more than half a century, this de Sitter model seemed to be only a mathematical curiosity, of no relevance to the real Universe; but it is now one of the cornerstones of inflationary cosmology.
When the general theory of relativity was published in 1916, de Sitter reviewed the theory and developed his own ideas in a series of three papers which he sent to the Royal Astronomical Society in London. The third of these papers included discussion of possible cosmological models -- both what turned out to be an expanding universe (the first model of this kind to be developed, although the implications were not fully appreciated in 1917) and an oscillating universe model.
De Sitter's solution to Einstein's equations seemed to describe an empty, static Universe (empty spacetime). But in the early 1920s it was realized that if a tiny amount of matter was added to the model (in the form of particles scattered throughout the spacetime), they would recede from each other exponentially fast as the spacetime expanded. This means that the distance between two particles would double repeatedly on the same timescale, so they would be twice as far apart after one tick of some cosmic clock, four times as far apart after two ticks, eight times as far apart after three ticks, sixteen times as far apart after four ticks, and so on. It would be as if each step you took down the road took you twice as far as the previous step.
This seemed to be completely unrealistic; even when the expansion of the Universe was discovered, later in the 1920s, it turned out to be much more sedate. In the expanding Universe as we see it now, the distances between "particles" (clusters of galaxies) increase steadily -- they take one step for each click of the cosmic clock, so the distance is increased by a total of two steps after two clicks, three steps after three clicks, and so on. In the 1980s, however, when the theory of inflation suggested that the Universe really did undergo a stage of exponential expansion during the first split-second after its birth, this inflationary exponential expansion turned out to be exactly described by the de Sitter model, the first successful cosmological solution to Einstein's equations of the general theory of relativity.
One of the peculiarities of inflation is that it seems to take place faster than the speed of light. Even light takes 30 billionths of a second (3 x 10(exp-10) sec) to cross a single centimetre, and yet inflation expands the Universe from a size much smaller than a proton to 10 cm across in only 15 x 10(exp-33) sec. This is possible because it is spacetime itself that is expanding, carrying matter along for the ride; nothing is moving through spacetime faster than light, either during inflation or ever since. Indeed, it is just because the expansion takes place so quickly that matter has no time to move while it is going on and the process "freezes in" the original uniformity of the primordial quantum bubble that became our Universe.
The inflationary scenario has already gone through several stages of development during its short history. The first inflationary model was developed by Alexei Starobinsky, at the L. D. Landau Institute of Theoretical Physics in Moscow, at the end of the 1970s -- but it was not then called "inflation". It was a very complicated model based on a quantum theory of gravity, but it caused a sensation among cosmologists in what was then the Soviet Union, becoming known as the "Starobinsky model" of the Universe. Unfortunately, because of the difficulties Soviet scientists still had in traveling abroad or communicating with colleagues outside the Soviet sphere of influence at that time, the news did not spread outside their country.
In 1981, Alan Guth, then at MIT, published a different version of the inflationary scenario, not knowing anything of Starobinsky's work. This version was more accessible in both senses of the word -- it was easier to understand, and Guth was based in the US, able to discuss his ideas freely with colleagues around the world. And as a bonus, Guth came up with the catchy name "inflation" for the process he was describing. There were obvious flaws with the specific details of Guth's original model (which he acknowledged at the time). In particular, Guth's model left the Universe after inflation filled with a mess of bubbles, all expanding in their own way and colliding with one another. We see no evidence for these bubbles in the real Universe, so obviously the simplest model of inflation couldn't be right. But it was this version of the idea that made every cosmologist aware of the power of inflation.
In October 1981, there was an international meeting in Moscow, where inflation was a major talking point. Stephen Hawking presented a paper claiming that inflation could not be made to work at all, but the Russian cosmologist Andrei Linde presented an improved version, called "new inflation", which got around the difficulties with Guth's model. Ironically, Linde was the official translator for Hawking's talk, and had the embarrassing task of offering the audience the counter-argument to his own work! But after the formal presentations Hawking was persuaded that Linde was right, and inflation might be made to work after all. Within a few months, the new inflationary scenario was also published by Andreas Albrecht and Paul Steinhardt, of the University of Pennsylvania, and by the end of 1982 inflation was well established. Linde has been involved in most of the significant developments with the theory since then. The next step forward came with the realization that there need not be anything special about the Planck- sized region of spacetime that expanded to become our Universe. If that was part of some larger region of spacetime in which all kinds of scalar fields were at work, then only the regions in which those fields produced inflation could lead to the emergence of a large universe like our own. Linde called this "chaotic inflation", because the scalar fields can have any value at different places in the early super-universe; it is the standard version of inflation today, and can be regarded as an example of the kind of reasoning associated with the anthropic principle (but note that this use of the term "chaos" is like the everyday meaning implying a complicated mess, and has nothing to do with the mathematical subject known as "chaos theory").
The idea of chaotic inflation led to what is (so far) the ultimate development of the inflationary scenario. The great unanswered question in standard Big Bang cosmology is what came "before" the singularity. It is often said that the question is meaningless, since time itself began at the singularity. But chaotic inflation suggests that our Universe grew out of a quantum fluctuation in some pre-existing region of spacetime, and that exactly equivalent processes can create regions of inflation within our own Universe. In effect, new universes bud off from our Universe, and our Universe may itself have budded off from another universe, in a process which had no beginning and will have no end. A variation on this theme suggests that the "budding" process takes place through black holes, and that every time a black hole collapses into a singularity it "bounces" out into another set of spacetime dimensions, creating a new inflationary universe -- this is called the baby universe scenario.
[to be continued]
The reason why the GUTs created such a sensation when they were applied to cosmology is that they predict the existence of exactly the right kind of mechanisms to do this trick. They are called scalar fields, and they are associated with the splitting apart of the original grand unified force into the fundamental forces we know today, as the Universe began to expand and cool. Gravity itself would have split off at the Planck time, 10-43 of a second, and the strong nuclear force by about 10(exp-35) of a second. Within about 10-32 of a second, the scalar fields would have done their work, doubling the size of the Universe at least once every 10-34 of a second (some versions of inflation suggest even more rapid expansion than this).
This may sound modest, but it would mean that in 1032 of a second there were 100 doublings. This rapid expansion is enough to take a quantum fluctuation 1020 times smaller than a proton and inflate it to a sphere about 10 cm across in about 15 x 1033 seconds. At that point, the scalar field has done its work of kick-starting the Universe, and is settling down, giving up its energy and leaving a hot fireball expanding so rapidly that even though gravity can now begin to do its work of pulling everything back into a Big Crunch it will take hundreds of billions of years to first halt the expansion and then reverse it.
Curiously, this kind of exponential expansion of spacetime is exactly described by one of the first cosmological models developed using the general theory of relativity, by Willem de Sitter in 1917. For more than half a century, this de Sitter model seemed to be only a mathematical curiosity, of no relevance to the real Universe; but it is now one of the cornerstones of inflationary cosmology.
When the general theory of relativity was published in 1916, de Sitter reviewed the theory and developed his own ideas in a series of three papers which he sent to the Royal Astronomical Society in London. The third of these papers included discussion of possible cosmological models -- both what turned out to be an expanding universe (the first model of this kind to be developed, although the implications were not fully appreciated in 1917) and an oscillating universe model.
De Sitter's solution to Einstein's equations seemed to describe an empty, static Universe (empty spacetime). But in the early 1920s it was realized that if a tiny amount of matter was added to the model (in the form of particles scattered throughout the spacetime), they would recede from each other exponentially fast as the spacetime expanded. This means that the distance between two particles would double repeatedly on the same timescale, so they would be twice as far apart after one tick of some cosmic clock, four times as far apart after two ticks, eight times as far apart after three ticks, sixteen times as far apart after four ticks, and so on. It would be as if each step you took down the road took you twice as far as the previous step.
This seemed to be completely unrealistic; even when the expansion of the Universe was discovered, later in the 1920s, it turned out to be much more sedate. In the expanding Universe as we see it now, the distances between "particles" (clusters of galaxies) increase steadily -- they take one step for each click of the cosmic clock, so the distance is increased by a total of two steps after two clicks, three steps after three clicks, and so on. In the 1980s, however, when the theory of inflation suggested that the Universe really did undergo a stage of exponential expansion during the first split-second after its birth, this inflationary exponential expansion turned out to be exactly described by the de Sitter model, the first successful cosmological solution to Einstein's equations of the general theory of relativity.
One of the peculiarities of inflation is that it seems to take place faster than the speed of light. Even light takes 30 billionths of a second (3 x 10(exp-10) sec) to cross a single centimetre, and yet inflation expands the Universe from a size much smaller than a proton to 10 cm across in only 15 x 10(exp-33) sec. This is possible because it is spacetime itself that is expanding, carrying matter along for the ride; nothing is moving through spacetime faster than light, either during inflation or ever since. Indeed, it is just because the expansion takes place so quickly that matter has no time to move while it is going on and the process "freezes in" the original uniformity of the primordial quantum bubble that became our Universe.
The inflationary scenario has already gone through several stages of development during its short history. The first inflationary model was developed by Alexei Starobinsky, at the L. D. Landau Institute of Theoretical Physics in Moscow, at the end of the 1970s -- but it was not then called "inflation". It was a very complicated model based on a quantum theory of gravity, but it caused a sensation among cosmologists in what was then the Soviet Union, becoming known as the "Starobinsky model" of the Universe. Unfortunately, because of the difficulties Soviet scientists still had in traveling abroad or communicating with colleagues outside the Soviet sphere of influence at that time, the news did not spread outside their country.
In 1981, Alan Guth, then at MIT, published a different version of the inflationary scenario, not knowing anything of Starobinsky's work. This version was more accessible in both senses of the word -- it was easier to understand, and Guth was based in the US, able to discuss his ideas freely with colleagues around the world. And as a bonus, Guth came up with the catchy name "inflation" for the process he was describing. There were obvious flaws with the specific details of Guth's original model (which he acknowledged at the time). In particular, Guth's model left the Universe after inflation filled with a mess of bubbles, all expanding in their own way and colliding with one another. We see no evidence for these bubbles in the real Universe, so obviously the simplest model of inflation couldn't be right. But it was this version of the idea that made every cosmologist aware of the power of inflation.
In October 1981, there was an international meeting in Moscow, where inflation was a major talking point. Stephen Hawking presented a paper claiming that inflation could not be made to work at all, but the Russian cosmologist Andrei Linde presented an improved version, called "new inflation", which got around the difficulties with Guth's model. Ironically, Linde was the official translator for Hawking's talk, and had the embarrassing task of offering the audience the counter-argument to his own work! But after the formal presentations Hawking was persuaded that Linde was right, and inflation might be made to work after all. Within a few months, the new inflationary scenario was also published by Andreas Albrecht and Paul Steinhardt, of the University of Pennsylvania, and by the end of 1982 inflation was well established. Linde has been involved in most of the significant developments with the theory since then. The next step forward came with the realization that there need not be anything special about the Planck- sized region of spacetime that expanded to become our Universe. If that was part of some larger region of spacetime in which all kinds of scalar fields were at work, then only the regions in which those fields produced inflation could lead to the emergence of a large universe like our own. Linde called this "chaotic inflation", because the scalar fields can have any value at different places in the early super-universe; it is the standard version of inflation today, and can be regarded as an example of the kind of reasoning associated with the anthropic principle (but note that this use of the term "chaos" is like the everyday meaning implying a complicated mess, and has nothing to do with the mathematical subject known as "chaos theory").
The idea of chaotic inflation led to what is (so far) the ultimate development of the inflationary scenario. The great unanswered question in standard Big Bang cosmology is what came "before" the singularity. It is often said that the question is meaningless, since time itself began at the singularity. But chaotic inflation suggests that our Universe grew out of a quantum fluctuation in some pre-existing region of spacetime, and that exactly equivalent processes can create regions of inflation within our own Universe. In effect, new universes bud off from our Universe, and our Universe may itself have budded off from another universe, in a process which had no beginning and will have no end. A variation on this theme suggests that the "budding" process takes place through black holes, and that every time a black hole collapses into a singularity it "bounces" out into another set of spacetime dimensions, creating a new inflationary universe -- this is called the baby universe scenario.
[to be continued]
