Gravitational Waves in the Cosmic Microwave Background

Major announcement coming!

[Update: Of course by now the announcement has come, of the discovery of signatures of gravitational waves in the cosmic microwave background by the BICEP2 experiment, more or less as the post below surmised. This follow-up post features the main result plots from the announcement.]

That much is clear, from this press release: on Monday at noon Eastern time, astronomers will “announce a major discovery.” No evidence from that page what the discovery actually is. But if you’re friends with a lot of cosmologists on Facebook/Twitter (or if you just read the Guardian), you’ve heard the rumor: the BICEP2 experiment has purportedly detected signs of gravitational waves in the polarization of the cosmic microwave background radiation. If it’s true (and the result holds up), it will be an enormously important clue about what happened at the very earliest moments of the Big Bang. Normally I wouldn’t be spreading rumors, but once it’s in the newspapers, I figure why not? And in the meantime we can think about what such a discovery would mean, regardless of what the announcement actually turns out to be (and whether the result holds up). See also Richard Easther, Résonaances, Sesh Nadathur, Philip Gibbs, Shaun Hotchkiss, and Peter Coles. At a slightly more technical level, Daniel Baumann has a slide-show review.

Punchline: other than finding life on other planets or directly detecting dark matter, I can’t think of any other plausible near-term astrophysical discovery more important than this one for improving our understanding of the universe. It would be the biggest thing since dark energy. (And I might owe Max Tegmark $100 — at least, if Planck confirms the result. I will joyfully pay up.) Note that the big news here isn’t that gravitational waves exist — of course they do. The big news is that we have experimental evidence of something that was happening right when our universe was being born.

BICEP2 at the South Pole.

BICEP2 at the South Pole.

Cosmic inflation is actually a pretty simple idea. Very early on–we’re not sure exactly when, but plausibly 10-35 seconds or less after the Planck time–the universe went through a phase of accelerated expansion for some reason or another. There are many models for what could have caused such a phase; sorting them out is exactly what we’re trying to do here. The basic effect of this inflationary era is to smooth things out: stuff like density perturbations, spatial curvature, and unwanted relics just get diluted away. Then at some point–again, we aren’t sure when or why–this period ends, and the energy that was driving the accelerated expansion converts into ordinary matter and radiation, and the conventional Hot Big Bang story begins.

Except that quantum mechanics says that we can’t completely smooth things out. The Heisenberg uncertainty principle tells us that there will always be an irreducible minimum amount of jiggle in any quantum system, even when it’s in its lowest-energy (“vacuum”) state. In the context of inflation, that means that quantum fields that are relatively light (low mass) will exhibit fluctuations. (Gauge fields like photons are an exception, due to symmetries that we don’t need to go into right now.)

So inflation makes certain crude predictions, which have come true: the universe is roughly homogeneous, and the curvature of space is very small. But the perturbations on top of this basic smoothness provide more specific, quantitative information, and offer more tangible hope of learning more about the inflationary era (including whether inflation happened at all).

There are two types of perturbations we expect to see, based on two kinds of light quantum fields that fluctuated during inflation: the “inflaton” field itself, and the gravitational field. We don’t know what field it is that drove inflation, so we just call it the “inflaton” and try to determine its properties from observation. It’s the inflaton that eventually converts into matter and radiation, so the inflaton fluctuations produce fluctuations in the density of the early plasma (sometimes called “scalar” fluctuations). These are what we have already seen in the Cosmic Microwave Background (CMB), the leftover radiation from the Big Bang. Maps like this one from the Planck satellite show differences in temperature from point to point in the CMB, and it’s these small difference (about one part in 105) that grow into stars, galaxies and clusters as the universe expands.


Then, of course, there are quantum fluctuations in the gravitational field: gravitational waves, or “gravitons” if you prefer speaking quantum-mechanically (sometimes called “tensor” fluctuations in contrast with “scalar” density fluctuations). It was in the early 80’s, soon after inflation itself came along, that several groups pointed out this prediction: Rubakov, Sazhin, and Veryaskin; Fabbri and Pollock; and Abbott and Wise. [Update: As Alessandra Buonanno points out in the comments, the idea that gravitational waves could be generated by quantum fluctuations in an expanding universe was investigated earlier by L. Grishchuk, Sov. Phys. JETP 40, 409 (1975), and A. Starobinsky, JETP Lett. 30, 682 (1979). Grishchuk was before inflation was invented, so the resulting wavelengths would have been much shorter (and unobservable in the CMB), but it’s the same underlying physics; Starobinsky actually had is own proto-inflationary model.] Just as an electromagnetic wave is an oscillation in the electric and magnetic fields that propagates at the speed of light, a gravitational wave is an oscillation in the gravitational field that propagates at the speed of light. We can detect electromagnetic waves because they would cause a charged particle to jiggle up and down; we could (in principle, though not yet in practice) detect gravitational waves because they alternately stretch things apart and then compress them together as they pass.

Gravitational waves from inflation are interesting for a couple of reasons. First, we know they should be there; gravitation certainly exists, and it’s a massless field. Second, there is a way to disentangle the gravitational waves from the density fluctuations, using the polarization of the CMB. This was noted in a flurry of papers from 1996 by different subsets of Seljak, Zaldarriaga, Kamionkowski, Kosowsky, and Stebbins: 1, 2, 3, 4, 5. Finally, how strong the gravitational waves are at different wavelengths reveals a great deal about the details of inflation — including one magic number, the energy density of the universe during the inflationary era.

Any kind of electromagnetic radiation, such as the microwaves we observe in the CMB, has a polarization. An electromagnetic wave is just a propagating ripple in the electric and magnetic fields, and we (somewhat arbitrarily) define the direction of polarization to be the direction in which the electric field is oscillating up and down. Of course when we observe many photons, the polarizations of each photon will often be pointing in random directions, giving a net effect that adds up nearly to zero. That’s the case in an ordinary incandescent bulb, and it’s almost the case for the CMB. But not quite. There is a tiny amount of residual polarization in the CMB, first discovered by the DASI telescope. (I helped organize the talk at the Cosmo-02 where the discovery of CMB polarization was announced. It was the Ph.D. thesis project for John Kovac, who is now on the faculty at Harvard and the PI on BICEP. I can brag that he took my cosmology class back in grad school.)

But there’s polarization, and there’s polarization. Even without any gravitational waves, the CMB would still be polarized, just due to the distortions brought about by ordinary density perturbations. That’s what DASI discovered. Happily, we can distinguish density-induced polarization (“scalar modes”) from gravitational-wave-induced polarization (“tensor modes”) by the shape of the polarization pattern on the sky.

b-modes A map of CMB polarization takes the form of little line segments on the sky — the direction of the net oscillation in the electric field. If you just have polarization at one point, that’s all the information available; but if you have a map of polarization over some area, you can decompose it into what are called E-modes and B-modes. (See this nice article from Sky & Telescope.) The difference is that B-modes have a net twist to them as you travel around in a circle. That sounds a little loosey-goosey, but there is a careful mathematical way of distinguishing between the two kinds.

Very roughly: density (scalar, inflaton) perturbations produce only E-mode polarization, whereas gravitational wave (tensor) perturbations produce B-mode polarization as well as E-modes. [Update: Thanks to asad and Daniel in comments for a correction here.] That’s why looking for the B-modes is such a big deal.

It’s also hard, for a number of reasons. When we said “very roughly,” we meant it — there are various effects other than gravity waves that can create B-modes, typically by taking some E-modes and messing with them. One such effect is gravitational lensing — the deflection of light by matter in between us and the CMB. Indeed, B-modes from lensing have already been detected twice, by the South Pole Telescope and by the PolarBEAR experiment.

But now the rumor is that the BICEP2 experiment has found a signature of honest-to-goodness B-modes from primordial gravitational waves. I won’t speculate about the details like the amplitude or the statistical significance, since we’ll find that out soon enough.

Let’s instead think just a little bit about what it would mean. Both density perturbations and gravitational-wave perturbations arise from quantum fluctuations generated during inflation, and the amount of perturbation depends on the energy scale E at which inflation happens, defined as the energy density to the 1/4 power. (I’m presuming here that inflation is the right story, but of course we don’t know that for sure.) But there’s a difference: for density perturbations, what actually fluctuates is some hypothetical inflaton field ϕ. That’s related to the energy density, but it’s not exactly the same thing; the actual density comes from the potential energy, V(ϕ). So measuring the density fluctuations (which we’ve done) doesn’t tell us the energy scale of inflation directly; it’s modulated by the unknown function V(ϕ). The flatter the potential, the larger the density perturbations. We can make educated guesses, which tend to put the energy scale E at around 1016 GeV (where a GeV is a billion electron volts, about the mass of the proton). That’s pretty darn close to the Planck scale of 1018 GeV, and basically equal to the scale of hypothetical grand unification, so you see why any empirical information we can get about physics at those scales is extremely interesting indeed.

Gravitational-wave perturbations are different. They are not modulated by some unknown potential; they are produced by inflation, and we observe them directly. In straightforward models of inflation, the amplitude of the gravitational waves is directly proportional to the inflationary energy scale. If this rumored measurement (and the inflationary interpretation) are correct, we would have data about a physical process just a bit below the Planck scale. Currently, our empirical knowledge of the early universe only stretches to about one second after the Big Bang, courtesy of primordial nucleosynthesis. Here we’re talking about pushing that to less than 10-35 seconds.

Now to get a bit quantitative. We can approximately describe a set of cosmological perturbations by two numbers: the overall amplitude A, and the “spectral index” or “tilt” n that tells you how the perturbations change from large wavelengths to shorter wavelengths. For the density perturbations, we have a fairly good handle on what these numbers are; the amplitude is about 10-5, and the spectral index is about 0.96. For historical reasons, density perturbations that are the same on all wavelengths are said to have nS = 1, while gravitational perturbations that are the same on all wavelengths are said to have nT = 0, where S is for “scalar” and T is for “tensor.” (I think it’s conceivable that the data are still compatible with nS = 1 rather than 0.96, but you really have to bend over backwards.) Finally, we often compare the gravitational-wave perturbations to the density perturbations by giving the ratio r = AT/AS of amplitudes (tensor divided by scalar).

Here are the best constraints as of Sunday March 16, 2014, from the Planck satellite. Horizontal axis is the tilt of the density perturbations, vertical axis is the ratio of gravitational-wave to density fluctuations. (Note that Planck hasn’t yet released polarization data, but even just the temperature fluctuations provide some constraints on the gravitational-wave amplitude.) The half-ellipse blobs at the bottom are the regions allowed by the data, and the various dots and lines are the predictions of different inflationary models.


So you see that pre-BICEP2, we’re quite comfortable with density perturbations that have a spectral index nS = 0.96 or so, and no tensor fluctuations at all (r = 0). From what I’m told, the only way BICEP should be able to get a really solid detection (five sigma) is if r is about 0.2. Which seems to be in a bit of tension with the limits plotted here (although admittedly they are only two-sigma error contours). But we don’t know yet, and there is a bit of room for slop; maybe the central value found by BICEP2 is around 0.2, but it’s consistent with 0.1, which would be perfectly fine.

What does it all mean? Most importantly, a gravitational-wave signal that big is … really big. It corresponds to an energy scale during inflation that is pretty darn high. It’s actually not so easy (although certainly possible) to come up with models that have such prominent gravitational waves. This goes back to something called the Lyth bound, after its discoverer David Lyth. The issue is that there is an interplay between the size of the density perturbations, the size of the gravitational-wave perturbations, and the total amount by which the inflaton field rolls during inflation. Very roughly, the amount of field rolling (in units of the Planck scale) is ten times the square root of r. So if r > 0.01, the inflaton ϕ rolled by more than the Planck scale during inflation. That’s not impossible — it’s just provocative. In string theory, for example, most candidates for the inflaton are periodic, with a period of about the Planck scale. [Update: at least, that’s been the conventional wisdom in certain quarters. See comment by Eva below.] So large r is hard to get. And r=0.2 is large indeed.

There are loopholes, of course. An intriguing one is axion monodromy inflation, which has been investigated by Eva Silverstein, Alexander Westphal, and Liam McAllister. Instead of having just one periodic field, they imagine multi-dimensional field spaces; then the inflaton can essentially wind around one direction several times before reaching the bottom of its potential, allowing for quite large effective field values.

More importantly than the prospects for any given model, however, this is great news for inflation itself. While it’s the starting point for much contemporary cosmological theorizing about the early universe, honest physicists are quick to admit that inflation has its conceptual problems. The prediction of gravitational waves is one of the strongest empirical handles we have on whether inflation actually happened, so if this result is announced like the rumors say (and it holds up) it will dramatically effect how we think about the earliest moments in the history of our universe. And if we succeed in measuring not only the amplitude of the gravitational waves but also their spectral index nT, there is a “consistency relation” that holds in simple models of inflation: r = -8nT. If that turns out to hold, it will be very hard indeed to deny that inflation happened. (Sadly, there are all sorts of non-simple models of inflation in which the consistency relation is violated, so if it doesn’t turn out to hold, we won’t really know one way or the other.)

There is always the possibility that a result is announced but it doesn’t hold up, of course. These are really hard measurements, with many ways to go wrong, even for experimenters as undoubtedly careful as the BICEP folks are. When the announcement is made, look not only for the claimed statistical significance, but also (as Eiichiro Komatsu has emphasized) for its robustness — does it show up in multiple frequencies (of radiation), as well as at multiple scales on the sky? Happily there are many competing experiments that will move very quickly to tell us whether this is on the right track. Science!

Updates soon. Very soon.

  1. Pingback: Primordial Gravitational Waves? | viXra log

  2. That’s probably the most comprehensive and readable summary of the BICEP2 discovery I’ve read so far – thanks for posting it!

    I’m a little puzzled though – if this is such a MAJOR discovery, why was there not so much excitement about the possibilities of the soon to be announced Planck polarisation results? Surely people realised primordial gravitational waves could also be found by Planck – so why so little excitement about the possibility of their discovery (at least I didn’t notice much hype on blogs, which I would have expected if , like now, Harvard are claiming a MAJOR discovery (and apparently inviting Guth and Linde to the announcement tomorrow))?

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  3. Very roughly: density (scalar, inflaton) perturbations produce E-mode polarization, whereas gravitational wave (tensor) perturbations produce B-mode polarization.

    As you know, it would be more correct to say that density perturbations produce only E-mode polarization, whereas gravitational wave (tensor) perturbations produce both E- and B-mode polarization. Your phrasing implies that gravitational waves only produce B.

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  4. Great post Sean. One or two comments — Tensor perturbations produce *BOTH* E and B-Modes, but B-modes are the smoking gun because they can’t be produced by scalar perturbations. Also, independent of the inflationary story, there was also the seminal paper of Polnarev noting the possibility of polarizing the CMB with a background of gravitational waves,….29..607P.

    Of course he did not make the connection between tensors and B (curl)-modes, but its still an important part of the story IMHO.

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  5. James — I think everyone thought that existing limits on $r$ were too low to make a discovery possible with Planck. Not sure if that will now change, though there are known issues with low-l Planck polarization (first polarization data release is rumored to only be high-l). Now the question is how you hide such a high $r$ in the temperature data — this would seem to require fairly large running of the scalar spectral index, which is hard to explain in slow-roll single field inflation.

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  6. Thanks Daniel,

    so this is a really unexpected gem of an observation by BICEP2 (if correct!)

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  7. asad and Daniel– You’re right, that’s misleading; I’ll fix it.

    James– Most of us were expecting limits from Planck — that’s why I made my bet with Max!

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  8. Thanks for a great summary! If this turns out to be robust detection, I’ll have to add some more material to the “evidence for GWs” section of my thesis…

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  9. I’m not a physicist, but I’ll bet you’re right. About 6 months ago new news articles on the subject started getting hard to find. Before that if someone sneezed while talking about gravitational waves it made it into an article.

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  11. Hi Sean,
    Great summary of this amazing physics, capturing all the different facets of the subject. Just one pedantic comment about the issue of large-field inflation in string theory.
    I don’t think we have a statement that most candidate inflatons are small field. Axion fields are generically lifted by monodromy (they are not periodic on a given branch of their potential, despite the underlying shift symmetry) in the presence of the fluxes and branes of string theory. This is true individually, and also for multiple fields (there is a previous idea known as N flation using multiple axions to obtain an effectively large range — this has a very red tilt, but maybe the most generic idea is multiple axions taking into account their monodromy). Now axion fields and their duals are an order one (or better) fraction of the scalar fields in string theory. In SUSY regimes, they are roughly half the fields, and in higher-dimensional starting points their number actually grows exponentially (like 2^D), dominating the spectrum. There is lore in the community that small field is more common, but I don’t get that. (The number of papers on it may be larger, but of course that’s a very different statement…).

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  12. Eva– Point taken. Small-field models are favored by conventional wisdom, but not by an actual reliable argument; I’ll update the post to reflect that.

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  13. Sean, you maybe missed one article in your list of blogs that have written about this
    More importantly, if this is truly a measurement of r=0.2, at l~100, then what Daniel pointed out is important. This will be indicating a large running of the scalar spectral index. This is something that models like “Axion Monodromy”, “Natural inflation”, “m^2\phi^2″, etc aren’t so keen to produce. It would also be implying that the (anomalous) deficit in scalar power on large scales is even more drastic than previously suspected.

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  14. Shaun– sorry, I actually did have your blog post open in a tab, but somehow didn’t include it. Until now!

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  15. Hi Sean , thanks for the great post.
    Robert H. Brandenberger had an interesting paper a few years ago saying that B modes were not unique to inflation:
    the real test would be ( if i understood the paper properly) to see if the gravity wave spectrum was red or blue titled. Do you think that a ground based experiment could determine this ?
    I note that on PRISM site they claim any ground based detection will need to confirmed from space and only a space based detector can get the required information.
    love to hear your thoughts on this Sean.

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  16. Hi Sean,

    nice summary.

    “It was in the early 80′s, soon after inflation itself came along, that several groups pointed out this prediction: Rubakov, Sazhin, and Veryaskin; Fabbri and Pollock; and Abbott and Wise.”

    As far as I know the first papers discussing it are in the 70s by L. Grishchuk, Sov. Phys. JETP 40, 409 (1974), and A. Starobinsky JETP Lett. 30, 682 (1979) [].

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  17. Alessandra– Thanks, I don’t know those papers (and I don’t have access to them at the moment). Did they really predict gravitational waves from inflation before inflation had been invented? (Would seem like a typical Russian thing to do.)

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  18. And Bruce would have been tickled too. I hope it is indeed a “robust” result. Thanks, Sean, for such a clear explanation too.

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  19. The key mechanism responsible of the production of gravitational waves during inflation is the amplification of quantum vacuum fluctuations, which is a very general mechanism in quantum-field theory in curved space-time. It was first discussed in cosmology in those papers.

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  21. Sean, love the post.

    Can you say that if primordial B-modes are found then inflation did happen?

    Are there other ways to achieve such B-modes (not the lensed B-modes, but true primordial B-modes)?

    If there are no primordial B-modes found (at whatever limits BICEP2 might have), would this be an indication that inflation did not happen?

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  22. Just a note of thanks for keeping us abreast of the latest in cosmology. Exciting times!

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  23. (phil h – just this moment saw your link to the Brandenberger paper – maybe that will answer my questions, the abstract looks very good!)

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  24. I have two comments.

    1) I think the direct detection (by Advanced LIGO) of gravitational waves from astrophysical sources would surely improve our understanding of the universe and it deserves a mention in your punchline.

    2) Among the early predictions of gravitational waves from inflation, surprisingly Alexei Starobinsky, the first one to predict (before the actual Inflationary theory), is missing (

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  25. Ok, so what do I tell my kid? 25 words or less, 5th grade level…

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  26. Would the BICEP2 results have any implications favoring one CDM theory over others?

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  29. Hi Sean, Alessandra,

    An English translation of Leonid’s 1974 paper can be found here:

    Paper talks about how gravitational radiation should necessarily be generated in the early Universe. It’s a real shame that Leonid is not here for this! If a detection of primordial gravitational waves were announced, he’d be ecstatic!

    A really nice blog post Sean! Hopefully going to be a really fantastic day. I’m looking forward to the scientific fallout from this!

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  32. Excellent summary!!, very beautifully explained a great concept of Physics.

    One can get large tensor to scalar ratio with sub-Planckian VEV models of inflation, one does not need super-Planckian VEV models of inflation, with inflection point: some detailed studies were performed here:
    and more recently:,
    Inflection point models of inflation can produce sup-Planckian VEV models of inflation and large tensor to scalar ratio: r.
    More over these models can be embedded within particle theory, such as the inflaton carries the SM charges, i.e. squarks and sleptons in SUSY SM.

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  33. Pingback: Inflation: fast or slow? | Going Past The Chemist

  34. I’m out of my depth here, but could the Higgs field undergoing spontaneous symmetry-breaking provide the energy for inflation?

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  35. Avoiding the math, one take from this announcement if it proceeds according to rumour is that the inflationary universe is a theoretical high probability. From another website … “In its basic form it predicts that our spacetime is physically infinite, and is filled everywhere with stars and galaxies just about like those we see within our own cosmic horizon (out to just 13.8 billion light-years in terms of look-back distance).”

    The only way our universe can be physically infinite (and NASA tends to agree with this – see “This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe.”) is if the inflationary period was so “extreme” that its “velocity” itself was infinite.

    Leaving the math (divisions by zero) – any explanations as to how our universe became “physically infinite”?

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  36. Hi Professor,

    Thanks for the great post. Just a few questions:

    1. Does inflation end before or after the “Big Bang?” In Max Tegmark’s book, he describes the Big Bang as the end of inflation in our part of space and as the Big Bang being the result of decaying inflationary substance.

    2. The inflationary period seems to end at 10-25 after the Big Bang yet universe is only 1cm in diameter. So inflation stops before the universe expands to infinite size?

    3. What are the implications for eternal inflation? Does inflation stop here but continue somewhere else? Do regions of space where inflation does not stop expand infinitely?

    Thanks very much.


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  39. @Daryl: there is something called Higgs inflation, where the Higgs field is the actual instanton field. For that to work you need to introduce a large so-called non-minimal coupling of the Higgs field to gravity (in the spirit of tensor-scalar theories). The resulting theory actually works very well with Planck data, but it tends to predict a pretty small tensor-to-scalar ratio.

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  40. @none – Here is an attempt (31 words)

    Gravitational waves are not waves _in_ space, but waves _of_ space(time), so they go through everything, allowing us to “see” the violence of the very early universe, which is otherwise completely hidden.

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  42. Thanks, Sean, for a very useful post and review. Much appreciated!

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  46. @Steve, David: Inflation is just an expansion for the sake of this analysis. The universe could have been infinite before (if inflation is a finite period) or under the expansion (if inflation is somewhere an indefinite long period; less likely, I guess). But as we only see the observable universe, the universe doesn’t need to be larger than ~ 1000 times that to fit observations, I think. (From Susskind’s cosmology lectures on youtube.)

    Isn’t the idea that inflation decided the size of the whole enchilada a variant of the “big bang is an explosion” error? The universe has several different expansion periods – inflation dominated, radiation dominated, matter dominated, dark energy dominated) – inflation is one of them (albeit an important one), none of them needs to have anything to do with how the size of the universe was decided (albeit they put a lower limit).

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  47. Well, I know MY physics geek tensor is fluctuating! Revenge of the physics nerds, Sean — the Irish lose out this time.

    Question***: Is this evidence “direct enough” that we should be sending our condolences to P.Steinhart & N.Turok??

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  49. I learned my physics and astronomy over 50 years ago, when it was a lot simpler; the Steady State vs Big Bang dispute was still going on.

    I have a possibly totally irrelevant question — does this have any implications for any of the multiverse theories?

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  51. Does the amount of inflation within the first fractions of a second suggest
    movements faster than light speed?

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  53. Thanks Sean for reminding me of our $100 bet, which I’d been trying my best to forget as the upper limits on r kept creeping down recently! It was really fun to see Alan & Andrei out-smiling one another at the press conference today!

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  57. My understanding is that the light itself that we are seeing has to come from after recombination (formation of atoms so light has a long mean free path), but that’s at about the 400,000 year mark. So, is what we are seeing the remains of the 400,000 year old gravitational waves that occurred during inflation? (That is, the light passing through those 400,000 year old gravitational waves picked up that level of polarization?)

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  58. Thanks for writing a non-technical introduction to the topic, which has gotten quite a lot of attention online; I’m a bit surprised that you neither mentioned the founder of inflation nor the groups that actually calculated these primordial fluctuations – if I recall correctly, they haven’t even been mentioned in the press conference. They are cited in the paper, though, and are quite serious contenders for a Nobel prize.

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  59. Nice summary Sean.

    If I may add to Anupam’s comment, the small field/sub-planckian inflationary models with large r were first suggested in:
    Another nice thing about them is that they inevitably predict a scale dependent spectral index, and enhancement of the power spectrum on small scales so they can be verified/falsified by other means such as CMB spectral distortions or SN lensing.
    1203.2681 and 1309.4771.

    Regarding Eva’s comment about the large field models in string theory, usually one needs a shift symmetry for that, so you can have at most N (fields) directions which have this shift symmetry, while for small field models all you need are an inflection point which you have much more in the string landscape. (I don’t remember the parametric dependence on N) Pedro & Westphal did some work on the statistical significance of that. This is a recent argument on why small field models are more “common”. One can also ask whether he “prefers” functional tuning or parameter tuning. On a related issue, are there any axion monodromy models with SUSY?

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  61. Is there any possibility a supermassive, infinitesimal spherical shell’s gravity, far from canceling out for an observer inside the sphere, could power inflation through some kind of pressure or repulsive force and that the signature of this continued pressure could show up as the cosmological constant?

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  62. Pingback: The First Direct Evidence of Inflation Found | Calli Arcale's Fractal Wonder

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  75. Thank you for this informing post.

    Though something puzzles me. Why did you refer to the 1993 Nobel Prize for Physics presse release as proof that gravitational waves exist when that raport explicitly states “The good agreement between the observed value and the theoretically calculated value of the orbital path can be seen as an indirect proof of the existence of gravitational waves. We will probably have to wait until next century for a direct demonstration of their existence.”?

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  78. Sean or anyone else. This is probably a naive question. Could you (or anyone else)
    send me the reference to the first paper(or textbook) where the theoretical B-mode
    spectrum from inflation (as a function of angular scale) is shown(basically the second figure)?

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  82. I love your final paragraph! It really gets at what science is all about: robust, testable measurements that require a detailed understanding of many subtly difficult aspects of the detector and theory. I feel like this message gets lost in many (typically sensationalist IMHO) pop science articles. Thanks for giving your readers such insight :)

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  84. Sean, I’d like to ask a question that has been burning a hole in my head for some time and which was revived when I read this and the Guardian article with all the talk about astronomical inflation. I came to this question a long time ago when reading about the square cube law and the literally incredible sizes of some creatures such as the Brachiosaurus and the Meganeura. The question that immediately came to mind was simply how do we know the fossils are still the same size as the creatures from which they were formed? Is it not possible that the universe, expanding as it is on the astronomical level, is not also expanding on smaller levels, such as the molecular or atomic? Is it not possible that everything has gotten bigger while mass has remained constant? This would explain why the fossils leave impressions of creatures which seem too big to move their own mass.

    Please accept my apologies if this is a stupid question. I am a calligrapher, not a physicist.

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  97. Munawar, that text is very vague and poetic and I struggle to see how it can be made to refer to something as specific and complex as gravitational waves. It’s like I offer you a cup which could just as easily contain coffee or Pepsi as it can milk, and you conclude from its shape that it must contain water taken early in the morning of 21 March 2014 from a specific spring in the Southern Cedarberg mountains just after the first rains of the season.

    Even if the words were written with miraculous prescience but shaped so as to cater for primitive minds which would not have understood them, they would have been more specific.

    And besides that, I think you drain the words of their poetic or religious value by taking them to have literal, physical reference. It’s like if I called you “enlightened” but what I really meant was not that you were wise and knowledgeable, only that someone had switched on the light in the room. To have used the word enlightened in such a way is in fact rather comical, and this is what you have done here to the words of the Koran – made them into a joke. Is that really what you want to do?

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