Inflation for Beginners

I was prompted to add this by recent debate about the cosmic background radiation. From my book Companion to the Cosmos.

inflation: General term for models of the very early Universe which involve a short period of extremely rapid (exponential) expansion, blowing the size of what is now the observable Universe up from a region far smaller than a proton to about the size of a grapefruit in a small fraction of a second. This process would smooth out spacetime to make the Universe flat (see flatness problem), and would also resolve the horizon problem.
Inflation became established as the standard model of the very early Universe in the 1980s. It achieved this success not only because it resolves many puzzles about the nature of the Universe, but because it did so using the grand unified theories (GUTs) and understanding of quantum theory developed by particle physicists completely independently of any cosmological studies. These theories of the particle world had been developed with no thought that they might be applied in cosmology (they were in no sense “designed” to tackle all the problems they turned out to solve), and their success in this area suggested to many people that they must be telling us something of fundamental importance about the Universe.
The marriage of particle physics (the study of the very small) and cosmology (the study of the very large) seems to provide an explanation of how the Universe began, and how it got to be the way it is. Inflation is therefore regarded as the most important development in cosmological thinking since the discovery that the Universe is expanding first suggested that it began in a Big Bang.
Taken at face value, the observed expansion of the Universe implies that it was born out of a singularity, a point of infinite density, 15 to 20 billion years ago. Quantum physics tells us that it is meaningless to talk in quite such extreme terms, and that instead we should consider the expansion as having started from a region no bigger across than the Planck length (10-35 m), when the density was not infinite but “only” some 1094 grams per cubic centimetre. The first puzzle is how anything that dense could ever expand — it would have an enormously strong gravitational field, turning it into a black hole and snuffing it out of existence (back into the singularity) as soon as it was born (see free lunch Universe).
Other problems with the Big Bang theory before the development of inflationary models involve the extreme flatness of spacetime (which means that the expansion of the Universe is balanced against the tug of gravity so that it sits precisely on the dividing line between expanding forever and one day recollapsing in a Big Crunch; see density prameter), and its appearance of extreme homogeneity and isotropy, most clearly indicated by the uniformity of the background radiation.
All of these problems would be resolved if something gave the Universe a violent outward push (in effect, acting like antigravity) when it was still about a Planck length in size. Such a small region of space would be too tiny, initially, to contain irregularities, so it would start off homogeneous and isotropic. There would have been plenty of time for signals travelling at the speed of light to have criss-crossed the ridiculously tiny volume, so there is no horizon problem — both sides of the embryonic universe are “aware” of each other. And spacetime itself gets flattened by the expansion, in much the same way that the wrinkly surface of a prune becomes a smooth, flat surface when the prune is placed in water and swells up. As in the standard Big Bang model, we can still think of the Universe as like the skin of an expanding balloon, but now we have to think of it as an absolutely enormous balloon that was hugely inflated during the first split second of its existence.
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 force by about 10-35 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 10-32 of a second there were 100 doublings. This 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 10-33 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.
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 10-10 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 10-33 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 travelling 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 (Physical Review, volume D23 page 347, January 1981). 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. Although there were obvious flaws with the specific details of Guth’s original model (which he acknowledged at the time), 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 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 realisation 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 the baby universe scenario.
There are similarities between the idea of eternal inflation and a self-reproducing universe and the version of the Steady State hypothesis developed by Fred Hoyle and Jayant Narlikar, with their C-field playing the part of the scalar field that drives inflation. As Hoyle wryly pointed out at a meeting of the Royal Astronomical Society in London in December 1994, the relevant equations in inflation theory are exactly the same as in his version of the Steady State idea, but with the letter “C” replaced by the Greek “”. “This,” said Hoyle (tongue firmly in cheek) “makes all the difference in the world”.
Modern proponents of the inflationary scenario arrived at these equations entirely independently of Hoyle’s approach, and are reluctant to accept this analogy, having cut their cosmological teeth on the Big Bang model. Indeed, when Guth was asked, in 1980, how the then new idea of inflation related to the Steady State theory, he is reported as replying “what is the Steady State theory?” But although inflation is generally regarded as a development of Big Bang cosmology, it is better seen as marrying the best features of both the Big Bang and the Steady State scenarios.
This might all seem like a philosophical debate as futile as the argument about how many angels can dance on the head of a pin, except for the fact that observations of the background radiation by COBE showed exactly the pattern of tiny irregularities that the inflationary scenario predicts. One of the first worries about the idea of inflation (long ago in 1981) was that it might be too good to be true. In particular, if the process was so efficient at smoothing out the Universe, how could irregularities as large as galaxies, clusters of galaxies and so on ever have arisen? But when the researchers looked more closely at the equations they realised that quantum fluctuations should still have been producing tiny ripples in the structure of the Universe even when our Universe was only something like 10-25 of a centimetre across — a hundred million times bigger than the Planck length.
The theory said that inflation should have left behind an expanded version of these fluctuations, in the form of irregularities in the distribution of matter and energy in the Universe. These density perturbations would have left an imprint on the background radiation at the time matter and radiation decoupled (about 300,000 years after the Big Bang), producing exactly the kind of nonuniformity in the background radiation that has now been seen, initially by COBE and later by other instruments. After decoupling, the density fluctuations grew to become the large scale structure of the Universe revealed today by the distribution of galaxies. This means that the COBE observations are actually giving us information about what was happening in the Universe when it was less than 10-30 of a second old.
No other theory can explain both why the Universe is so uniform overall, and yet contains exactly the kind of “ripples” represented by the distribution of galaxies through space and by the variations in the background radiation. This does not prove that the inflationary scenario is correct, but it is worth remembering that had COBE found a different pattern of fluctuations (or no fluctuations at all) that would have proved the inflationary scenario wrong. In the best scientific tradition, the theory made a major and unambiguous prediction which did “come true”. Inflation also predicts that the primordial perturbations may have left a trace in the form of gravitational radiation with particular characteristics, and it is hoped that detectors sensitive enough to identify this characteristic radiation may be developed within the next ten or twenty years.
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Further reading: John Gribbin, In the Beginning.

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One comment on “Inflation for Beginners

  1. Ian Liberman says:

    I love reading about eternal and chaotic inflation and the history of inflationary theory. Thanks for this excellent piece. Could you write a piece one day on the Casimir effect when you time?

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