While some theories and theorists got even bangier, others were banged in their heads



Update: on Friday, Nature will publish a rather helpful and complementary article about spring cleaning after the BICEP2 announcement.



In this blog post, I will assume that the observation of BICEP2 suggesting \(r\approx 0.20\pm 0.05\) and \(n_s\approx 0.96\pm 0.01\) is right and will eventually be confirmed by independent experiments. If the result turns out to be wrong, the whole blog post below will become irrelevant and misleading, but so will many other, more important texts and papers. That was the last time I mentioned this disclaimer in this text; I think that e.g. Matt Strassler's addition of "IF IF IF" in several colors in each sentence of his long text is a somewhat childish pose. Moreover, I think that the discovery is more likely to be right than wrong.



This new discovery is groundbreaking and has a huge impact on the health of virtually all detailed models of inflation and its audaciously proposed alternatives. Let me list some major losers and winners; I expect some true expert in inflationary model building to do a similar job "right".







The #1 loser: cyclic and ekpyrotic universes



Throughout the recent decades, Paul Steinhardt and Neil Turok were the two loudest critics of cosmic inflation. (Well, we could also include Roger Penrose, but that would bring us too far from science to science-fiction.) Most of the TRF blog posts mentioning Turok and many of those mentioning Steinhardt refer to these men's vigorous attacks against cosmic inflation.



They would be repeating that inflation doesn't solve the problems that inflation solves so beautifully and they would be proposing various cyclic and ekpyrotic (born from fire) alternatives to inflation. What is the status of this competition? Well, let them speak. Look at their 2003 paper with Justin Khoury. They wanted to show some "really bad news" for inflation. Let me quote the abstract:



We present a simple, nearly model-independent estimate that yields the predictions of the simplest inflationary and ekpyrotic/cyclic models for the spectral tilt of the primordial density inhomogeneities. Remarkably, we find that the simplest models yield an identical result: \(n_s\) is approximately \(0.95\). For inflation, the same estimate predicts a ratio of tensor to scalar contributions to the low multipoles of the microwave background anisotropy of T/S \(r=20\%\); the tensor contribution is negligible for ekpyrotic/cyclic models.



% To complete the synthesis, we need unification at the unification (= inflation!) scale. So: Seek SUSY, desperately! [See] Unification of Couplings



So the cyclic and ekpyrotic models are so cool because they predict negligible tensor modes. Eleven years later, an experiment measures T/S \(r=20\%\), exactly what Turok et al. assigned to inflation. The spectral index \(n_s\) predicted for inflation is consistent with the observed one within 1 sigma, too.The agreement between the "prediction of simple inflationary models" quoted negatively in a critical paper and the observation is amazingly ironic. It reminds me of the cute 2008 story when Alain Connes calculated from some of his "noncommutative standard models" that the Higgs had to weigh \(170\GeV\). Needless to say, \(170\GeV\) was exactly the first a priori possible Higgs mass that was excluded by the Tevatron! ;-) So I would say that cyclic and ekpyrotic cosmologies in all of their known sufficiently studied incarnations are just dead. The "cyclic/ekpyrotic vs inflation" debate could have looked like one of the religious debates that may never be settled. Some people who like to be hostile towards science would suggest that inflation isn't science, and so on. But it is a damn good science. Theories make predictions and the cyclic/ekpyrotic models predicted "negligible tensor modes" and this prediction has apparently been falsified.Yummy. If you're keeping a list of inflation-like candidate papers to describe the Universe, you may probably throw all the papers co-authored by Steinhardt, Turok, Ovrut (sorry, Burt), and several others into the trash bin now. If you're on the board of the Perimeter Institute, you should start to think how to formulate the letter in which you fire Neil Turok from the chair of the director. Be sure he is like a sticky tick that won't resign himself; he is already " urging caution " on BICEP2 and he clearly plans to do so indefinitely. It's OK to be wrong but if you promote something to the mission of your life and you're wrong, I guess that it should have consequences. Cosmic inflation as a paradigm and its earliest co-father Alan Guth is of course the main winner but I want to be a bit more specific.Andrei Linde's "chaotic inflation" uses the simple quadratic potential \(V=\frac 12 m^2\phi^2\) for the inflaton field. It predicts \(n\approx 0.96\), exactly the mean value measured by BICEP2, and \(r\approx 0.16\), less than one sigma below the measured central value \(r\approx 0.20\). Linde's model is remarkably simple and I tend to think that it will be viewed as the inflationary counterpart of the Standard Model's simple Higgs sector.(The same model also makes the inflation "almost inevitably" eternal which means that the BICEP2 result strengthens the case for the multiverse – as it disfavors some possible objections against the multiverse – but of course the BICEP2 result by itself is in no way sufficient to "prove" the multiverse. And it is surely not enough to legitimize the anthropic reasoning which is yet another level.) Liam McAllister wrote a wonderful text explaining that the inflaton field had to move by "more than the Planck mass" to achieve the inflation that produces these strong tensor modes. This is a problem because at these high changes of the scalar field, the quantum-gravity or other corrections are expected to invalidate the effective field theory. Liam has sketched some strategies to avoid this problem. Matthew Reece of Harvard wrote a post-discovery analysis and dedicated some space to a stringy " [axion] monodromy inflation " which may also circumvent the problem.One of the other strategies to circumvent the "Lyth bound problem" was posted (today) in the first hep-ph paper that already takes the BICEP2 result into account (it was probably written when this information was "just a rumor"). Nakayama and Takahashi claim that the quadratic chaotic inflation is fine and now the well-known Higgs field may play the role of the inflaton as long as its kinetic term is modified for large values of \(h\sim \phi\). The modification is rather simple:\[\LL = \frac 12 \zav{ 1+\xi \phi^2 } ( \partial \phi)^2 - V(\phi).\] The unification of the Higgs and the inflaton seems economical but it is surely not among the "widely studied mainstream ideas" and it will probably avoid the mainstream, anyway, because a "new field operating at the very high, inflation/GUT scale, seems to be almost directly following" from the BICEP2 discovery. It's my guess that the Higgs=inflaton loophole should be looked at, anyway.Using a more political attitude, the #1 winner is the Big Oil. The core of the funding for BICEP/Keck ($2.3 million) was provided by the Keck Foundation named after William Myron Keck, the founder of the Superior Oil Company that became a part of ExxonMobil. So everyone who likes the yesterday's result should praise the Big Oil! I surely do even though I haven't received a penny from them. But I did receive my share of the excitement. Adam Falkowski mentioned another possible huge "political" loser: the Planck experiment that has so far overlooked this low-hanging Nobel-prize-winning fruit even though the experiment costs EUR 0.7 billion, over 100 times more than the BICEP experiment.I was thinking for a while which paradigm would make it to the second place, after the clear ekpyrotic/cyclic "winners among the losers". Finally, Archil Kobakhidze whom you know as the author of a paper debunking Verlinde's entropic gravity by showing that it destroys the (experimentally observed) interference of neutrons in the gravitational field (an argument I wrote independently of Archil in this blog) told us about his interesting January 2013 paper written along with Alexander Spencer-Smith In that paper, they were already assuming that the tensor modes would be found. Such tensor modes prove that the scale of inflation is high enough and at such high energy scales, the metastability of the Higgs boson (which may hold in the Standard Model) becomes a straight instability. Note that the anti de Sitter space (like in AdS/CFT) allows "somewhat tachyonic" particles, above the (negative) Breitenlohner-Freedman (BF) bound. On the contrary, the de Sitter space (approximately the spacetime during inflation) renders even some positive-mass particles effectively "tachyonic" and therefore inconsistent, and this is the case of the "too light" Higgs boson, too.I tend to believe that this paper is basically correct and the Standard Model of particle physics is excluded as the right theory up to the scale of inflation by the BICEP2 data. So even though both the discovery of the Higgs boson and the B-modes seem to favor some "really simple theories", the discovery by the BICEP2 also disfavors and maybe kills the simplest theory (still) suggested by the LHC at low energies.People have made tons of tweets about BICEP2, some of them linked to articles on this blog, and I have only retweeted a few tweets. My most favorite tweet was coming from the Twitter named Frank Wilczek , a co-father of QCD and a Nobel Prize winner. I actually liked all of his recent tweets but 15 hours ago, he wrote the following:The document he linked to was his article with Savas Dimopoulos and Stuart Raby in Physics Today, October 1991. I was still just a high school student but they already outlined the most tasteful grand unified, supersymmetric theory. You may check on page 33 that the unification in the supersymmetric grand unified theory appears around the scale \(10^{16}\GeV\), and it happens to be nearly equal to the scale of inflation suggested by the BICEP2 discovery. So the unification and inflation scales are the same assuming that supersymmetry holds.This coincidence of the unification and inflation scales has actually been discussed for decades. It seems natural from many viewpoints. There may be a big desert between the LHC scale (or a bit higher one) and the GUT scale but new fields have to arise at the GUT scale (like the GUT-breaking Higgs fields) and there's no reason why the inflaton shouldn't be a part of this GUT package. Within the string-theoretical incarnations, one also typically expects that the string scale is "just a little bit higher" than the GUT scale, but still beneath the nearby Planck scale.(However, see Roby's comments in the comment section [he is a reader from CERN] – there is a possible problem about the "scale of inflation" as the energy density changes with time during inflation and "the" observed value isn't necessarily the most fundamental one. In particular, the mass in the quadratic coefficient is lower than the GUT scale by two orders of magnitude. I admit that he may have a point. Nevertheless, I do think that there's something nontrivial about the data which apparently make the inflation scale as high as possible a priori, a point that was also stated by Matt Strassler .)Those things look totally consistent and one may argue that the observed tensor-to-scale ratio \(r\) was really "predicted" by SUSY GUT. So the main remaining goal is to actually find SUSY. Look for SUSY desperately. Just to be sure, the words "desperately seeking" are popular among particle physicists. Many authors wrote papers called "Desperately Seeking SUSY" (or something else) – most famously, Ginsparg and Glashow wrote "Desperately Seeking Superstrings" in 1986. All these names are parodies of a 1985 comedy-drama film "Desperately Seeking Susan".So yes, there are reasons to think that the supersymmetry and unification haters should start to look for the backdoors to escape in a similar way as Paul Steinhardt and his cyclic colleagues.A related justification for another "winner" or some "losers" is the comment that the scale of inflation seems to be maximized among the a priori allowed ones. So this evidence really suggests that the quantum gravity scale is close to \(10^{19}\GeV\), the traditional four-dimensional Planck scale, which therefore disfavors or rules out "large extra dimensions" (ADD) as well as "old extra dimensions" (Randall-Sundrum). Thanks to Steve Hsu for reminding me about this omission. So although these models are primarily models of particle physics, they could be viewed as major losers, too. The usual quantum gravity with the naive (very high) Planck scale seems to be a major winner.I wasn't sure whether I would promote the 2004 paper by Barrau and Ponthieu but I wanted to add some balance, i.e. skepticism towards supersymmetry here. In that paper, they argued that if the tensor modes are found, and they have apparently been found, the cosmological constant is very high. In minimal (and perhaps not just minimal) SUGRA, the gravitino mass is linked to the cosmological constant and it comes out in the forbidden interval where the gravitino is light enough to exist and heavy enough to "hit" and destroy some successful predictions of the Big Bang Nucleosynthesis. There are several assumptions here and I am not able to quickly organize all the thoughts in my head. I hope that an expert will do it in a more rigorous blog post.Robert Brandenberger of McGill argues that the blue tilt suggested by the BICEP2 results disfavors inflation and agrees with some predictions of the string gas cosmology that has been marketed as a competitor to inflation, too. Recall that the defining "virtue" of string gas cosmology is that wrapped strings (or, in the brane gas cosmology, branes) may prevent some dimensions from expanding, and 3+1 large dimensions might be predicted by a dynamical mechanism in which the strings try to unwrap themselves (annihilate with the oppositely wound ones). Just to be sure, I would assign the inflation-less string gas cosmology at least 100 times lower priors than to the proper cosmic inflation but it is conceivable that they have a point.Robert Brandenberger wrote some papers with Cumrun Vafa of Harvard , Ali Nayeri, and sometimes other co-authors. I was watching them as they were preparing those papers, it was fun, so even though I don't quite see how these models may replace all the desirable functions that cosmic inflation is apparently able to play, I am ready to think that they got a small positive boost by the BICEP2 data, so their paradigm has surely not been eliminated in the same way as the cyclic and ekpyrotic Universes. Robert is planning a post-BICEP2 short preprint about string gas cosmology and may contribute a guest blog, too (perhaps the same text, perhaps not).The graph above was posted by Adam Falkowski on Friday, when the BICEP2 was just a rumor. He told us to be ready that the graph would change. The horizontal axis shows the primordial tilt, the spectral index measured to be around \(n_s=0.96\pm 0.01\). The vertical axis shows the tensor-to-scalar ratio.The shaded bump-like areas represent the allowed 68% and 95% regions recommended by the experiments before BICEP2. They were hills sitting on the ground because the experiments before BICEP2 were compatible with \(r=0\), the ground level. The colorful dumbbells and some of the colorful strips show predictions of various inflationary models. The smaller disk at the end of each dumbbell corresponds to the inflation with 50 \(e\)-foldings; the larger one corresponds to 60 \(e\)-foldings.All these Planck-dominated hill-like bumps got taller (more tolerant) in the graphs of the BICEP2 collaboration because the BICEP2 collaboration had to allow for a "running spectral index", i.e. allow \(n_s\) to depend on the wave number \(k\). With this extra freedom to adjust, Planck excludes less and tolerates taller "hills". But let's use Adam's Friday graph above, anyway. The new result by BICEP2 favors a circle around \(r=0.20\pm 0.05\) whose center sits strictly above the highest bump. So without the "running spectral index", the mean value of BICEP2 would contradict the Planck exclusion limits by about 3 sigma. This looks dramatic but one must understand that the right value could very well be e.g. \(r=0.15\) which agrees with BICEP2 within one BICEP2-defined sigma; and with the Planck exclusion limits within 2 Planck sigmas. So even without the running spectral index, the contradiction wasn't really serious. (It will get serious if Planck reports more accurate data that will still suggest \(r=0\).)So you see that the new BICEP2 circle, flying above the hills, is compatible with the \(V\sim \phi^3\) inflation (green dumbbell) and with the \(V\sim \phi^2\) quadratic inflation (the black dumbbell; Andrei Linde's chaotic inflation, already discussed as the main winner in this blog post) – and remotely with the "natural inflation" as long as it is close enough to the quadratic inflation (the upper boundary of the curved violet strip). A special point of the "power law inflation" – that seemed to contradict the Planck exclusion data – could be revived but I find it unlikely.All the other models listed in the graph, namely \(V\sim \phi^n\) with \(n=2/3\) and \(n=1\) and the \(R^2\) inflation, seem to be at least in some conflict with the BICEP2 discovery, much like the hilltop quartic model (greenish strip). So while cosmic inflation as a paradigm has incredibly strengthened on Monday March 17th, most of the detailed models of inflation are really in trouble. Science works like that: a class of theories strengthens when most of the members of the class are exterminated. This idea may sound counter-intuitive for nations but it works for classes of theories.The text above is written by someone who is no real expert in inflation model building but it could be interesting for some readers, anyway, and a more accurate judgment written by an expert could come soon.