## Monday, March 24, 2014

### Alan Guth and inflation

Alan Guth of MIT is one of the nine well-deserved inaugural winners of the Milner Prize. He has received \$2,999,988 because Milner failed to pay the banking fees (Alan Guth was generous enough not to have sued Yuri Milner for that so far).

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

Originally posted on August 28th, 2012

1. It humans didn't have merely ten fingers, but instead had a thousand tentacles, our counting system would not suffer an overwhelming 46 “orders of magnitude” divide between subatomic and cosmic realms, but only 15. On standard copier paper, if the 11 inch height is marked out with a thousand lines, they are about a hundredth of an inch apart, something any thin little machinist pocket ruler has visible divisions for too, perfectly clear to anybody with normal vision. So it's just *fifteen* of those pages, each shrunken in between two lines of the next page, to encompass all of creation, and only *eight* pages between ourselves and either extreme. The awe factor of Powers Of Ten books and documentaries seem willfully overblown, merely counting by powers of ten instead of more intuitively useful powers of a thousand. That we already have microscopes that can image individual atoms (only three pages away) is indication that extreme scales are not really so intractably alien.

2. How is connected the 10-base logarithm to the number of humans fingers? With 10 fingers you can count to 1024, so 1024 based system is more natural for people. (Despite the fact that English-speaking humans have only 8 fingers.)

3. I would bet that the final theory contains nothing like the inflation(of course that doesn't mean it is useless). Because there is so much uncertainty in closely related concepts, i.e. quantum gravity, dark energy, unification. I can easily imagine one of them predicting a working big bang theory, or one that needs a completely different correction than the inflation.

4. Dear Bill, your comment is utterly irrational, especially if one considers the timing. It's like a guy who - after Magellan returns from his trip around the Earth - points out that he believes that the explanation has to be completely different than a round Earth because there are so many uncertainties about our flat Earth.

5. Lubos,

Thanks for this wonderfully informative post, perfect with morning coffee. Your blog has very definitely rekindled my interest in cosmology, which, sadly, was barely smoldering from my long ago college days. BTW, the finest discussion of the naturalness of e (2.178…) that I am aware of was given by Walter Rudin in the Prologue to his “Real and Complex Analysis”.

6. Looking at Guth's (ahem) slightly slovenly appearance, it is no wonder he is reputed to have the messiest office in the visible universe. I'll find a link to that if necessary. (I'll nominate myself for coming in second.)

7. Strange, I don't find his appearance slovenly at all. ;-)

8. But you have to admit that a flat earth would be highly desirable from a real estate point of view. :)

9. "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 the even messier scale in the middle where human beings take over.

10. kashyap vasavadaMar 24, 2014, 3:39:00 PM

Interesting picture Lubos. In U.S. if you show one finger to someone, you have a good chance of getting shot! I wonder if that is true in Italy or Europe!

11. kashyap vasavadaMar 24, 2014, 4:26:00 PM

Nice review Lubos: I am interested in your comment "new inflation may possibly be incompatible with string theory." In the new inflation do you include Linde's chaotic inflation?

12. Dear Kashyaap, yes, Linde's chaotic inflation is surely the top example of "new inflation". More generally, "new inflation" is anything from Linde and those who consider his contribution to be progress from Guth's "old inflation".

I wrote this some years ago. The incompatibility is really about an "order of magnitude estimate" but there are now known loopholes, e.g. monodromy inflation

within string theory so the sharp incompatibility seems unlikely.

13. Linde then moves forward by mathematical construct that such B modes may termed to be gravitational waves as a form of naturalness. That continues to point toward multiverse then?

Secondly, the historical journey of B modes is important and to see that linked adds to the discussion for me.

Thanks,

14. "An exemption from the energy conservation law" Noether's theorems couple conserved currents to continuous symmetries. Conservation of mass-energy requires homogeneous time. It was untrue through inflation. It isn't true today - gravitational potential wells, confirmed by GPS satellites' atomic clocks versus ground clocks. Type I perpetual motion machines remain elusive.

Conservation of angular momentum requires exactly isotropic vacuum. This is true for boson photons and untrue for fermionic matter (hadrons). Vacuum is trace chiral anisotropic toward matter as parity violations, symmetry breakings, chiral anomalies, Chern-Simons repair of Einstein-Hilbert action. Notherian leakage toward matter is Milgrom acceleration (arXiv:1310.4009, 0906.0668). Dark matter is curve fitting.

Planck: 13.82 Gyr; 68.3% dark energy, 26.8% dark matter, 4.9% baryonic matter. arXiv:1306.5534, dark matter inside Saturn's orbit is less than 1.7×10^(-10) M_solar. Physics assumes absolute conservation laws. FAIL

15. Sorry if this is a stupid question, but I've never really understood the horizon problem. Wasn't the universe homogeneous immediately after the big bang? What's the source of the expected anisotropies that we fail to see in the CMB?

16. Dear Wanda, immediately after the Big Bang, the different places of the Universe could hardly agree about anything - like the density or temperature - because they were spacelike separated and they even didn't have any "shared events" in the intersection of their light cones because the Universe was just born.

The causal relationships in the Universe according to ordinary Big Bang Theory are faithfully captured by the Penrose diagram

https://higgs.ph.ed.ac.uk/sites/default/files/penrose-deSitter.jpg

where the diagonal 45-degree lines are light-like. The Big Bang t=0 moment is the horizontal line at the bottom. So the different regions just couldn't have "thermalized" - or otherwise interacted.

Of course, it's plausible that the initial singularity has a "law of physics" that guarantees the same conditions everywhere but a priori, it's more likely that this is false.

Inflation modifies the Penrose diagram by making it taller. Because of the inflationary era, the points at the beginning of the normal power-law expansion actually do share some points in the interaction of their past light cones.

17. I think that R.H. Dicke of Princeton was the first person to discuss the flatness and horizon problems. Not surprising since the had studied GR carefully and had his own version of GR, the Brans-Dicke theory, though he eventually gave up and accepted Einstein’s version. In fact, he had predicted a CMBR of < 20K right after WWII. See http://en.wikipedia.org/wiki/Discovery_of_cosmic_microwave_background_radiation. He, Wilkson, and Peebles were searching for the CMBR when Penzias and Wilson made the discovery.

18. Dear Lubos

Is there any connection between inflation and and anti-desitter space in Ads/CFT. Could we be a 4-D Ads with some hidden supersymmetry inside a huge 3-D SU(N) CFT at the outer edge of space-time. Or maybe black holes are the CFT's that connect to one big messy 4-D Ads.

19. Hi Physics Junkie, maybe you think about some connection I don't quite get, but let me say the following: there is a much more direct connection between inflation and de Sitter space (dS) with the anti. An inflating Universe does resemble the de Sitter space. In many respects, it's very different from AdS. AdS may preserve SUSY, dS cannot. AdS is static in some coordinates, dS is never static, and so on, and so on. They have different boundaries, too.

Andy Strominger would also coin dS/CFT as opposed to AdS/CFT. It has boundaries at "time at plus minus infinity" and I don't think that it works at the same level of satisfaction as AdS/CFT.

20. Wasn't the singularity a shared event?

I understand that spacelike separations prevent temperature differences from equilibrating. My question is about the origin of the temperature differences to begin with. It seems to me that every piece of the early universe was subject to the same laws of physics and started at the same singularity. In other words, same boundary conditions + same dynamics = homogeneous everywhere. I don't understand how that symmetry gets broken. Is it simply quantum fluctuations?

21. Dear Wanda, I understand where you're coming from.

After all, inflation itself may be interpreted as a proof-of-a-concept of (y)our comment that general initial conditions may imply the same conditions.

But it's still right to say that the Big Bang singularity was *not* a shared event. The Big Bang singularity is a spacelike (3D, Euclidean signature) submanifold of the spacetime, so it's not just one point. It's a whole hyperplane of points. If supplemented with normal laws of the Big Bang without inflation, one doesn't expect a thermal ensemble at all, and if there is a thermal beginning, it would still be non-uniform and had huge fluctuations because the super-young Universe was still much "wider" than "older" (it was spacelike), so any wave - like the quantum fluctuations - would create lots of inhomogeneities.

These are the problems that inflation resolves. Before BICEP, one could have viewed these problems to be a matter of taste, and deny that they were problems, and you're clearly inclined to think in this direction. BICEP, if correct, may be considered direct evidence of inflation because the observed tensor waves are very large - hundreds of millions of light years - and must come from some waves that followed some laws and had tensor indices, and quantum-fluctuating tensor field during inflation when these cosmic sizes were really small seems to be the only explanation, one that agrees perfectly.

22. Thanks for clearing that up.

23. Yes, but I feel more like the guy who points out that just because you traveled around the Earth, it doesn't prove that it is a *cylinder*. There has to be a more elegant explanation for that.

Actually, eternal inflation(http://arxiv.org/abs/hep-th/0702178) I think it is worse than that. It is like traveling around the earth and saying: "Well, we know that the Earth is flat, but now I traveled a long time and I see a land exactly like the one I left. So everything on the Earth's surface has to repeat itself infinite times."

24. Lubos, thank you very much for your (and your guest bloggers') excellent treatments of the BICEP2 results and their implications.

Inflation has always seemed "likely to have happened" to me because it so efficiently/elegantly solves seemingly disjoint problems. I never really internalized this belief, though; it was always a kind of nice intellectual game and not much more. But near the end of this article I was struck by a kind of awe at the prospect of the universe actually having undergone this process, and all the implications thereof. I haven't had that feeling in quite a while, and it was a nice reminder of why I got into science in the first place. Thanks again.

I am hoping that Prof. Brandenberger will chime in with a string gas cosmology perspective on these results. While the blue tilt in the BICEP2 results seems suggestive, it's not clear to me what, if anything, can be said about the (detailed, not just roughly scale-invariant) CMB anisotropy spectrum, and whether or not more ingredients are needed to deal with flatness.

25. After a re-read this was a bit arrogant.Congratulations to Alan Guth, I am perfectly sure that he advanced theoretical physics by a great deal, I just hope it is not the end of the story.

26. She is not "Hot" - she is a LASH - Leftwing Anticivilisation Socialist Hypocrite