As far as I know, Alan Guth is the only winner of a prize greater than the Nobel prize who has ever regularly attended a course of mine. ;-)
I have taken many pictures of Alan Guth, this is the fuzziest one but I think it's funny to see a young Italian physicist showing a finger to Alan Guth in the New York Subway during our trip to a May 2005 conference at Columbia University.
Under the name Alan H. Guth, the SPIRES database offers 73 papers, 51 of which are "citeable". That's fewer than some other famous physicists have but the advantage is that it keeps Alan Guth in the rather elite club of physicists with about 200 citations per average paper.
For quite some time, Guth would work on rather typical problems of particle physics, the science of the very small, but he of course became one of the main symbols of modern cosmology, the science of the very large. Note that the LHC probes distances comparable to \(10^{-20}\) meters while the current radius of the visible universe is about \(46\) billion light years which is \(4.4\times 10^{26}\) meters.
Every distance scale comes with its own set of physical phenomena, visible objects, and effective laws, and it may look very hard to jump over these 46 orders of magnitude from the very short distance scales to the very long distance scales and become a leader of a different scientific discipline. And indeed, it is rather hard. However, Nature recycles many physical ideas at many places so the "ideological" distance between the short and long distance scales is much shorter than the "numerical" distance indicates. Fundamental physicists are the rulers of the vast interval of distance scales (except for some messy phenomena in the middle where folks such as biologists may take over for a while).
And yes, Alan Guth's most famous discovery was a very important piece of "reconciliation" between physics of very short distances and physics of very long distances – a fascinating idea that put their friendship on firmer ground. (We're not talking about quantum gravity here which is what we do if we talk about the "stringy reconciliation"; gravity is treated classically or at most semiclassically in all the discussions about inflation.) Guth was thinking about the Higgs field – a field that became very hot this summer – and he realized it could help to solve some self-evident problems in cosmology.
By finding a speedy bridge between the world of the tiny and the world of the large, Guth has also explained where many large numbers comparing cosmology and particle physics such as "the number of elementary particles in the visible Universe" come from. These large numbers were naturally produced during an exponentially, explosively productive ancient era in the life of our Universe, an era in which the Universe acted as "the ultimate free lunch", using Guth's own words. Yes, cosmology has acquired an exemption from the energy conservation law. While people who study inflation usually say that there's nothing such as a free lunch (if they're economists, including Alan G[reenspan]), and they're "mostly" right, their colleague Alan Guth knows better.
Two papers by this author have over 1,000 citations. The pioneering 1980 paper on cosmic inflation has collected over 4,000 citations so far; Guth's 1982 paper with S.Y. \(\pi\) on fluctuations in new (i.e. non-Guth) inflation stands at 1,300+ now. Three more papers above 250 citations are about scalar fields, phase transitions, and false vacuum bubbles. All the papers are on related topics but they're inequivalent.
Old inflation: first look at the paper
Of course, I want to focus on his most famous paper whose content began to be discovered in 1979,
The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems (scanned PDF via KEK, full text)Rotate the PDF above in the clockwise direction; these commands are available via the right click in the Chrome built-in PDF reader, too.
Some people make a breakthrough but they present the idea in a confusing way and other people have to clean the discovery. I think that Guth's paper is different. It may be immediately used in the original form. It highlights the awkward features of the old-fashioned Big Bang Theory in a very modern way, pretty much the same one that people would talk about today, 30 years later; it sketches the basic strategy how to solve them; and it lists some undesirable predictions of his model of "old inflation" that could perhaps be solved by future modifications. If you read the paper in a certain way, you might conclude that everyone else who did research on inflation was just solving some homework exercises vaguely or sharply defined by Guth. He or she was filling holes in a skeleton constructed by Alan Guth.
Problems of TBBT
If you use the term "The Big Bang Theory" in the less popular sense – i.e. if you are talking about a cosmological theory, not a CBS sitcom – you will find out that despite all the advantages, the theory has some awkward features (unlike Sheldon Cooper who doesn't have any).
Alan Guth correctly identified two main problems of TBBT: the horizon problem and the flatness problem. I am no historian and at the end of 1979, I was affiliated with a kindergarten so I can't tell you how much people were confused about the disadvantages of TBBT in the late 1970s. But it's clear that Alan Guth wasn't confused.
The horizon problem
The horizon problem is the question why the cosmic microwave background radiation discovered by Penzias and Wilson in 1964 seems to have a uniform temperature around 2.7 kelvins, with the relative accuracy of 0.001% or so, even though the places in different directions of the heaven where the photons were originally emitted couldn't possibly have communicated with each other because they were too far from each other and the speed of light is the universal cosmic speed limit (for relative speed of two information-carrying objects moving past each other).
The limitations on speed are relevant because the Penrose causal diagram of the spacetime in TBBT looks like the picture above. Observers and signals have to move along timelike or lightlike trajectories which are, by the definition of the Penrose diagram, lines on the Penrose causal diagram that are "more vertical than horizontal", i.e. at most 45 degrees away from the vertical direction.
But at the moment of the Big Bang, and this moment is depicted as the lowest horizontal "plate" on the picture, the Universe had to be created and there was no prehistory that would allow the different places of the ancient Universe to agree about a common temperature. You might object that the Universe "right after \(t=0\)" was smaller so it could have been easier to communicate (shorter distances have to be surpassed). But you also had a shorter time between \(t=0\) and the other small value of \(t\) and if you study these things quantitatively, you will realize that the latter point (shortage of time) actually becomes more important than the smallness of the distances (because the distances go like \(a\sim t^k\) for \(k\lt 1\) so they're "more constant" than the time, relatively speaking), so to agree about a common temperature, two places in the Universe would need an ever higher speed of communication which surely exceeds the speed of light \(c\).
In other words, two events at \(t=0\), the horizontal plate at the bottom of the picture, had "no common ancestors" i.e. no other events in the intersection of their past light cones – because there was no "past" before the Big Bang (sorry, Bogdanov brothers and others) – so it's puzzling why the temperature is uniform if the different regions of the Universe were "created by God" independently from others.
Alan Guth proposed a solution: if the Universe has ever been exponentially expanding for a long enough time i.e. by a high enough factor, the Penrose diagram effectively becomes much taller – it looks like we are adding a whole "pre-Big-Bang prehistory" below the bottom plate at the picture above – and suddenly there is enough room to prepare the thermal equilibrium by the exchange of heat. So with this "taller" Penrose diagram, the equal magnitude of temperature in different directions is no longer mysterious: it is a result of a relatively long period of thermalization i.e. exchange of heat that inevitably erases the temperature differences.
To successfully achieve this goal (and especially the "flatness goal" to be discussed later), we need a certain amount of time for the thermalization: the universe has to increase about\[
e^{62} \approx 10^{27}
\] times, i.e. a billion of billions of billions of times. Appreciating that \(2.718\) is a more natural base of exponentials than ten (because Nature has \(e\) and not ten fingers as humans or two fingers as the discrete physicists), physicists say that there had to be at least \(62\) \(e\)-foldings. An \(e\)-folding is a period of time during an exponential expansion in which linear distances increase \(e\) times. The required minimum varies but 60-65 is what people usually consider the minimum (but there's nothing wrong with thousands of \(e\)-foldings, either, and many models on the market actually predict even higher numbers). I only chose \(62\) so that I could have written "billion of billions of billions". ;-)
So the distances \(a\) between two places in the sky as defined by the FRW coordinates, i.e. between two "future galaxies", grew \(10^{27}\) times during inflation; the remaining multiplicative growth was due to the ordinary Big Bang Theory growth (which approximately follows power laws, \(a\sim t^k\)). But because the growth was exponential, the proper time that inflation took was just \(62\) of some basic natural units of time: a natural, small number.
You see that the exponential growth is what allows cosmology to "quickly connect" very different distance scales and time scales. If you can expand the distances \(10^{27}\) times very quickly, it's easy to inflate a subatomic object to astronomical distances within a split second. That's cool. The uniformity of the temperatures suddenly becomes much more natural (even though you could have waved your hands and say that God created different regions of the Universe in similar conditions even if they couldn't have communicated with each other – because He has some universal initial conditions that just hold everywhere).
A reader could protest that we cheated because we "explained" the unnatural features of the Universe by using large numbers that are calculated as exponentials and the exponentials themselves are "unnatural". However, the latter assertion is incorrect. The exponentials are actually totally natural in the inflationary context. It's because the FRW equations, Einstein's equations simplified for the case of a homogeneous and isotropic expanding Universe, imply that the distance \(a\) between two future (or already existing) galaxies obeys\[
\ddot a = \dots + \frac{\Lambda c^2}{3} a.
\] Einstein's equations control the second time derivative of \(a\) – which emerges from the second derivatives of the metric tensor that is hiding in the curvature tensors – and the equation for the second derivative of the distance \(a\) is analogous to an equation in the Newtonian physics, \(ma=F\), for the acceleration of an object. In the FRW case, the force on the right hand side contains a term proportional to the cosmological constant \(\Lambda\) as well as \(a\) itself. And you may verify that the equation \(\ddot a = K a\) has solutions that are exponentially increasing (or decreasing, but the increasing piece ultimately dominates unless you fine-tune the exponentially growing component exactly to zero).
Well, the exponentially increasing/decreasing functions are solutions for \(K\gt 0\) i.e. \(\Lambda\gt 0\), a positive cosmological constant. For \(K\lt 0\), the solutions are sines and cosines because the equations describe a harmonic oscillator. (That's also why a negative cosmological constant \(\Lambda\) would tend to produce a Big Crunch – a sign that the Universe would like to resemble an oscillatory one.) You may see that if you had a spring with a negative (repulsive) spring constant, it would shoot the ball attached on the spring exponentially.
It's because the derivative (and the second derivative) of the exponential function is the exponential function (times a different normalization) in general. I hope you know the joke about functions walking on the street. Suddenly, the derivative appears behind the corner. All functions are scared to hell. Only one of them is proudly marching on the sidewalk. The derivative approaches the function and asks: Why aren't you afraid of me? I am \(e^x\), the function answers and moves the derivative by one unit of distance away from itself (because the exponential of the derivative is the shift operator, because of the formula for the Taylor expansion).
Sorry if I made the joke unfunny by the more advanced Taylor expansion piece. ;-)
Fine. The exponential (the exponentially increasing proper distance between the seeds of galaxies) is a totally natural solution of the basic universal equations – of nothing else than Einstein's equations expressed in a special cosmological context. It's not cheating. It's inevitable physics.
Flatness problem
Concerning the flatness problem, I may recommend you e.g. this question on the Physics Stack Exchange plus my answer.
Einstein's equations say that the spatial slice \(t={\rm const}\) through the Universe is a flat 3D space if the average matter density is close to a calculable "critical density", or their ratio \(\Omega=1\). However, it may be derived that \(|\Omega-1|\), the (dimensionless) deviation of the density from the value that guarantees flatness, increases with time during the normal portions of TBBT (which are either radiation-dominated or, later, matter-dominated).
Observations today show that the \(t=13.7\) billion years slice is a nearly flat three-dimensional space – the curvature radius is more than 1.5 orders of magnitude longer than the radius of the visible Universe (i.e. the curvature radius is longer than hundreds of billions of light years) – so \(|\Omega-1|\leq 0.01\) or so today. But because this \(|\Omega-1|\) was increasing with time, we find out that when the Universe was just minutes or seconds old (or even younger), \(|\Omega-1|\) had to be much more tiny, something like \(10^{-{\rm dozens}}\). Such a precisely fine-tuned value of the matter density is unnatural because \(|\Omega-1|\) may a priori be anything of order one and it may depend on the region.
Our Universe today seems rather accurately flat – I mean the 3D spatial slices – and you would like to see an explanation. You would expect that the flatness is an inevitable outcome of the previous evolution. However, TBBT contradicts this explanation. In TBBT, the deviations from flatness increase with time, so when the Universe was very young, the Universe had to be even closer to exact flatness by dozens of orders of magnitude, so it had to be even more unnatural when it was young than it is today! It had to be unbelievably unnaturally flat.
Again, cosmic inflation solves the problem because it reverses the trend. During cosmic inflation, \(|\Omega-1|\) is actually decreasing with time as the Universe keeps on expanding. So a sufficiently long period of inflation is again capable of producing the Universe in an unusually "nearly precisely flat" shape and some of its exponentially great flatness may be wasted in the subsequent power-law, TBBT expansion that makes the flatness less perfect. But the accuracy with which the Universe was flat after inflation was so good that there's a lot of room for wasting.
Inflation also solves other problems. For example, it dilutes exotic topological defects such as the magnetic monopoles. If you watch TV, you must have noticed that Sheldon Cooper's discovery of the magnetic monopoles near the North Pole was an artifact of a fraudulent activity of his colleagues. It seems that the number of magnetic monopoles, cosmic strings, and other topologically nontrivial objects in the Universe around us is much lower than what a generic grand unified theory would be willing to predict. Inflation makes the Universe much larger and the density of the topological defects decreases substantially, pretty much to \(O(1)\) defects per visible Universe. It's not too surprising that none of these one or several defects moving somewhere in the visible Universe has managed to hit Sheldon Cooper's devices yet.
So Alan Guth realized that the exponentially increasing period is a very natural hypothesis about cosmology beyond (i.e. before) the ordinary Big Bang expansion which helps to explain previously unnatural features of the initial conditions required by the ordinary Big Bang expansion. He also realized that the cosmological constant needed for this exponential expansion may come from a scalar field's potential energy density \(V(\phi)\). That's where his particle physics experience turned out to be precious: it's just enough to consider the potential energy for the Higgs field \(V(h)\), realize that its positive value has the same impact on Einstein's equations as a positive cosmological constant – they're really the same thing, physically speaking, because you may simply move the cosmological constant term \(-(1/2)Rg_{\mu\nu}\) to the right hand side of Einstein's equations and include it as a part of the stress-energy tensor. And he had to rename the Higgs field to an inflaton.
Guth's original "old inflation" assumes that the inflaton sits at a higher minimum of its possible values i.e. its "configuration space" during inflation and it ultimately jumps to a different place (the place we experience today) where the cosmological constant is vastly lower.
Now, the exponential expansion had to be temporary because we know that in the most recent 13.7 billion years, the expansion wasn't exponential but it followed the laws of the Big Bang cosmology. So the state of the Universe had to jump from a place in the configuration space with a large value of \(V(\phi)\) to another place with a tiny value of \(V(\phi)\). In Guth's "old inflation", it would literally be a discontinuous jump. In a year or two, "new inflation" i.e. "slow-roll inflation" got popular and started to dominate the inflationary literature. In the new picture, the inflaton scalar field continuously rolls down the hill from a maximum/plateau (the upper inflationary-era position is no longer a local minimum of the potential in that "new inflation" picture but it isn't necessarily a catastrophe) it occupies during inflation to the minimum we experience today. When it's near the minimum, its kinetic energy is converted to oscillations of other fields, i.e. particles that become seeds of the galaxies.
The very recent 8 years in cosmology and especially in string theory have shown that "new inflation" may possibly be incompatible with string theory. The very condition of the "slow-rollness", the requirement that the inflaton rolls down (very) slowly which is needed for the inflation to last (very) long, might be incompatible with some rather general inequalities that may follow from string theory. It's the main reason that has revived the interest in the "old inflation": the transition from inflation to the post-inflationary era could have been more discontinuous than "new inflation" has assumed for decades and physicists may be forced to get back to the roots and solve the problems of "old inflation" differently than by the tools that "new inflation" had offered.
Averaged fluctuations of the CMB temperature as a function of the typical angular scale: theory agrees with experiments.
These comments rather faithfully reflect the amount of uncertainty about inflation. The observations of the cosmic microwave background made by WMAP satellite – and even more recently, the Planck spacecraft – are in excellent, detailed agreement with the theory that needs TBBT as well as the nice, flat initial conditions, as well as some initial fluctuations away from the flatness that are naturally calculable within the inflationary framework.
So the pieces probably have to be right.
However, there are many technical details – about the mass scale associated with the inflaton (it may be close to the GUT scale but it may be as low as the electroweak scale: there are even models using the newly discovered Higgs field as the driver of inflation although they need some extra unusual ingredients); about the number of inflaton scalar fields; about their detailed potential; about the question whether any quantum tunneling has occurred when the inflationary era ended; whether the scalar field should be interpreted in a more geometric way (e.g. the distance between branes, some quantity describing the evolving shape of the hidden dimensions etc.); and other things.
But it is fair to admit that I would say that exactly the general features that were discussed in Alan Guth's pioneering paper have already been empirically established. The Nobel prize is nevertheless awarded for "much more directly" observed discoveries so it's great that Yuri Milner has created the new prize in which the "theory-driven near-complete certainty" plays a much larger role than it does in Stockholm.
And that's the memo.
Previous article about the Milner Prize winners: Ashoke Sen
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