Eternal inflation and the end of time

Inflating the Universe
It was only after the standard Big Bang idea was firmly established as a good description of the Universe, at the end of the 1960s, that cosmologists began to worry seriously about various cosmological coincidences, including the facts that space is very nearly flat with the density of the Universe close to critical, and that the distribution of matter across the Universe is incredibly smooth on the largest scales, but contains irregularities just the right size to allow for the growth of things like galaxies, stars, planets and ourselves.  According to the Big Bang model, these properties were already imprinted on the Universe at the time of the Big Bang, when the Universe was one ten-thousandth of a second old and everywhere was as dense as the nucleus of an atom today.  As the evidence mounted that the Universe we see around us has indeed emerged from such a hot fireball, the question of how these properties got imprinted on it became more pressing.  They had hardly mattered when people hadn’t been sure if there really had been a Big Bang; but now people began to try to work out what the Universe had been like at even earlier times, when it was hotter and denser, in an effort to find out what had set it up in the Big Bang to develop in the way it has.
     This quest involved taking on board ideas from high energy particle physics, using theories based on the results of experiments carried out at high energy particle accelerators.  These are the experiments and theories that suggest, for example, that entities such as protons and neutrons are actually made up of smaller entities known as quarks, and that the description of all the forces of nature can be combined into one mathematical package.  It turned out that in order to understand the Universe on the very largest scales it was first necessary to understand the behaviour of particles and forces (fields) on the very smallest scales and the highest energies.
     To put this in perspective, the kind of energies reached by particle accelerators in the 1930s correspond to conditions that existed in the Universe when it was a little over three minutes old; the accelerators of the 1950s could reach energies that existed naturally everywhere in the Universe when it was a few hundred-millionths of a second old; by the end of the 1980s, particle physicists were probing energies that existed when the Universe was about one tenth of a thousand-billionth of a second (10-13 sec) old; and the new Large Hadron Collider at CERN, near Geneva, is designed to reproduce conditions that existed when the Universe was only 5 x 10-15 of a second old – a fraction of a second indicated by a decimal point followed by 14 zeroes and a 5.
     There is no need to go in to all the details here, but one crucial point is that the distinction between the four kinds of force that are at work in the Universe today becomes blurred at higher energies.  At a certain energy, the distinction between the electromagnetic force and the weak force disappears and they merge into a single electroweak force; at a higher energy still, the distinction between the electroweak force and the strong force disappears, making what is known as a grand unified force;1 and it is speculated that at even higher energies the distinction between these combined forces and gravity disappears.
     As far as the early Universe is concerned, higher energies existed at earlier times.  So the suggestion is that at the Planck time there was just one superforce, from which first gravity, then the strong force, then the weak force split off as the Universe expanded and cooled.  How does that help us?  Because, as one young researcher realised at the end of the 1970s, this cooling and splitting off of forces could be associated with a dramatic expansion of the Universe, taking a volume of superdense stuff much smaller than a proton and whooshing it up to the size of a grapefruit in a tiny split-second.  That grapefruit was the hot fireball, containing everything that has become the entire visible Universe today, that we call the Big Bang.
     The researcher was Alan Guth, then (1979) working at MIT, who was a particle theorist who had become interested in the puzzle of the Big Bang.  He realised that there is a kind of field, known as a scalar field, which could have been part of the primordial quantum fluctuation, and would have had a profound effect on the behaviour of the very early Universe.  It happens that the pressure produced by a scalar field is negative.  This isn’t as dramatic as it sounds – it only means that this kind of pressure pulls things together rather than pushing them apart.  A stretched elastic band produces a kind of negative pressure, although we usually call it tension.  But the negative pressure associated with a scalar field can be very large, and it does have something exotic associated with it – negative gravity, which makes the Universe expand faster (this is essentially the same effect, but on a more dramatic scale, as the cosmological constant associated with the present much slower acceleration of the universal expansion).
     Guth realised that the presence of a scalar field in the very early Universe would make the size of any part of the Universe – any chosen volume of space – double repeatedly, with a characteristic doubling time.  This kind of doubling is called exponential growth, and very soon runs away with itself.  What Guth did not know at the time, but which made his ideas immediately appealing to cosmologists, was that this kind of exponential expansion is described naturally by one of the simplest solutions to Einstein’s equations, a cosmological model known as the de Sitter universe, after the Dutchman Willem de Sitter, who found this solution to Einstein’s equations in 1917.
     When Guth plugged in the data from Grand Unified Theories, he found that the characteristic doubling time associated with the scalar field ought to be about 10-37 sec.  This means that in this remarkably short interval any volume of the early Universe doubles in size, then in the next 10-37 sec it doubles again, and again in the next 10-37 sec, and so on.  After three doublings, that patch of the Universe would be eight times its original size, after four doublings 16 times its original size, and so on.  After n doublings, it is 2n times its original size.  Such repeated doubling has a dramatic effect.  It requires just 60 doublings to take a region of space much smaller than a proton and inflate it to make a volume about the size of a grapefruit, and 60 doublings at one every 10-37 sec takes less than 10-35 sec to complete.
     If we are lucky, the LHC will probe energies that existed when the Universe was 10-15 sec old.  There may not seem to be much difference between 10-15 and 10-35, but that’s because we naturally look at the difference between 15 and 35 and think it is “only” 20; it is actually a factor of 1020; that means that at 10-15 sec the Universe was already  a hundred billion billion times older than it was at  10-35 sec.  Putting it another way, the difference between 10-15 and 10-35 is actually 105 times (one hundred thousand times) bigger than the difference between 1 and 10-15.  So there is no hope of probing these energies directly in experiments here on Earth – the Universe itself is the test bed for our theories.
     This is all based on Guth’s original figures.  Some modern versions of inflation theory suggest that the process may have been slower, and took as long as 10-32 seconds to complete; but that still means that Guth had discovered a way to take a tiny patch of superdense stuff and blow it up into a rapidly expanding fireball.2  Even with this more modest version  of the expansion, it would be equivalent to taking a tennis ball and inflating it up to the size of the observable Universe now in just 10-32 seconds.  The process comes to an end when the scalar field “decays,” giving up its energy to produce the heat of the Big Bang fireball and the mass-energy that became all the particles of matter in the Universe.
     The initial, and continuing, appeal of inflation is that it explains many of the cosmic coincidences.  The huge stretching of space involved in 60 or so doublings smooths out irregularities in much the same way that the wrinkly surface of a prune is smoothed out when the prune is put in water and expands.  If it doubled in size 60 times (imagine a plum about a thousand times the size of our Solar System), if you were standing on its surface you would not even be able to tell the difference between the surface being very slightly curved rather than completely flat, just as for a long time people living on the surface of the Earth thought that it must be flat.  In other words, inflation forces the density of the Universe to be indistinguishably close to critical.
     The smoothing is imperfect because during inflation “ordinary” quantum fluctuations will produce tiny ripples which themselves get stretched as inflation continues.3  So the distribution of matter in the form of galaxies across the Universe today is only an expanded version of a network of quantum fluctuations from the first split-second after time zero.  Statistically speaking, the pattern of galaxies on the sky does indeed match the expected pattern for such fluctuations, a powerful piece of evidence in favour of the inflation idea.  Many other cosmic coincidences can also be explained within the framework of inflation, since if our entire visible Universe has inflated from a region much smaller than a proton, there may be many other universes that inflated in a similar way but are forever beyond our horizon.  And they need not all have inflated in the same way – perhaps not even with the same laws of physics.

Eternal Inflation and Simple Beginnings
The idea of what is now known as eternal inflation occurred to Alex Vilenkin in 1983.  He realised that once inflation starts, it is impossible for it to stop – at least, not everywhere.  The most natural thing for the inflation field to do is to decay into other forms of energy and ultimately matter; but within any region of inflating space, thanks to quantum uncertainty there will be variations in the strength of the scalar field, so that in some rare regions it actually gets stronger, and the rate of inflation increases.  Within that region itself, the most natural thing for the inflation field to do is to decay into other forms of energy and ultimately matter; but, thanks to quantum uncertainty there will be variations in the strength of the scalar field, so that in some rare regions of that region it actually gets stronger, and the rate of inflation increases.  The whole pattern repeats indefinitely, like a fractal.
     In a statistical sense, there are very many more places where inflation stops and bubble universes like our own (or unlike our own!) develop; but because inflation generates a lot of space very quickly, the volume occupied by inflating regions greatly exceeds the volume occupied by the bubbles.  Although there is a competition between the decay of scalar field producing bubbles devoid of inflation and rare fluctuations making more inflation, the latter are totally dominant.  Vilenkin likens this to the explosive growth of a culture of bacteria provided with a good food supply.   Bacteria multiply by dividing in two, so they have a typical growth rate, overall, with a characteristic doubling time – exponential growth, just like inflation.  Some bacteria die, when they are attacked by their equivalent of predators.  But if the number being killed is less than a critical proportion of the population, the culture will continue to grow exponentially.  Within the context of inflation the situation is slightly different – the regions that keep on inflating are rare statistically but overwhelmingly dominant in terms of the volume of the meta-universe they occupy.  Because there are always quantum fluctuations there will always be some regions of space that are inflating, and these will always represent the greatest volume of space.
     Vilenkin’s colleagues were initially unimpressed by his idea, and although he published it, he didn’t pursue it very actively in the 1980s and 1990s.  One of the few people who took the idea seriously was Andrei Linde, who developed it within the context of his idea of chaotic inflation, published a paper on the subject in 1986, and coined the name eternal inflation.  In 1987, using the word “universe” where I would use “meta-universe,” he wrote that “the universe endlessly regenerates itself and there is no global ‘end of time’  .  .  .  the whole process [of inflation] can be considered as an infinite chain reaction of creation and self-reproduction which has no end and which may have no beginning.”4  He called this “the eternally existing chaotic self-reproducing inflationary universe.”  The idea still wasn’t greeted with much enthusiasm, and although Linde promoted it vigorously eternal  inflation only really began to be taken seriously in the early years of the twentyfirst century, after the discovery of evidence for dark energy and the acceleration of the expansion of the Universe.
     All the evidence now points to the likelihood that our Universe will keep on expanding forever, at an accelerating rate.  The process is exactly like a slower version of the inflation which produced the bubble of space we live in.  Eventually – and it doesn’t matter how long it takes since we have eternity to play with – all the stars will die and all the matter of the Universe will either decay into radiation or be swallowed up in black holes.  But even black holes do not last forever.  Thanks to quantum processes, energy leaks away from black holes in the form of radiation.  This happens at an accelerating rate, and eventually they disappear in a puff of gamma rays.  So the ultimate fate of our Universe is to become an exponentially expanding region of space filled with a low density of radiation.  This is exactly the situation described by the solution to Einstein’s equations found by de Sitter, and known as de Sitter space.
     De Sitter space is the perfect breeding ground for inflation.  Within de Sitter space, quantum fluctuations of the traces of radiation and the scalar field we call dark energy will produce a few, rare Planck-scale regions that inflate dramatically to grow into bubble universes like our own.  And once you have inflation, then, as Vilenkin and Linde told us more than two decades ago, you have eternal inflation.  The discovery of the universal acceleration and its associated cosmological constant link us both with the future and the past of eternal inflation, possibly in a chaotic meta-universe.  It suggests that our Universe was born out of de Sitter space, and will end up as de Sitter space.  It’s just like starting over – and over, and over, and over again.  

Adapted from my book In Search of the Multiuverse

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