Anatomy of a Paper: Part III, Culmination

By Sean Carroll | July 31, 2007 6:41 pm

After being inspired in Part One and sweating through some calculations in Part Two, we’ve assembled all the ingredients of a good paper. We have an interesting question: “What would happen if there were a preferred spatial direction during inflation?” We have suggested a robust answer — an expression for the generalized power spectrum of density fluctuations — and calculated its observable effects. And then we proposed one specific model, lending credence to the idea that this is a sensible scenario to contemplate. Next it’s time to write the paper up, and then it’s cocoa and schnapps all around.

Which we proceeded to do, of course. Except that, as we were writing, there was something nagging at the back of my brain. We were thinking like field theorists, coming up with an idea (“a preferred direction during inflation”) and exploring how it could be constrained by data. But weren’t there people out there engaged in the converse — looking at the data and asking what it implies? Why, yes, there were. In fact, it gradually occurred to me, there was already a claim on the market that the actual CMB data were indicating a preferred direction in space! This had totally slipped my mind, in the excitement of exploring our little idea. (As the professional cosmologist of the collaboration, remembering such things was implicitly my job.)

The claim that there actually is evidence for a preferred direction in the CMB goes by the clever name of the axis of evil. If one looks closely at the observed anisotropies on the very largest scales, two interesting facts present themselves. First, there is less anisotropy than one would expect, on very large angular scales. Second, and somewhat more controversially, the anisotropy that does exist seems to be oriented along a certain plane in the sky, defining a preferred direction perpendicular to that plane. This preferred direction has been dubbed the “axis of evil.”

Is the axis of evil real? That depends on what one means by “real.” It does seem to be there in the data. On the other hand, maybe it’s just a fluke. Nobody has a theory that predicts CMB anisotropy directly as a function of position on the sky — rather, theories like inflation probabilistically predict the amplitude of anisotropy on each angular scale. But at each scale there are only a fixed number of independent observations one can make, implying an irreducible uncertainty in ones predictions — that was the original definition of cosmic variance, before we re-purposed the phrase. For what it’s worth, the actual plane in the sky defined by the large-scale anisotropy seems to coincide with the ecliptic, the plane in which the various planets orbit the Sun. Many people believe it’s just some local effect, or an artifact of a particular way of reducing data, or just a fluke — to be honest, nobody knows.

What’s relevant to the present discussion is that the very existence of the axis of evil phenomenon meant that other people had already been asking about preferred spatial directions in the CMB, even before our seminal work that didn’t yet quite exist. This fact dawned on me in the middle of our writing, and I started digging through the A of E literature. Lo and behold, I found a few of the equations of which we were so proud, especially in the work of Gumrukcuoglu, Contaldi, and Peloso. They had, in fact, derived a few of the equations of which we were justifiably proud.

But not all of them! We had, in other words, been partially scooped, although not entirely so. This is a remarkably frequent occurrence — you think you’re working on some project for esoteric reasons that are of importance only to you, only to find that similar tendencies had been floating around in the air, either recently or some number of years prior. Occasionally the scoopage is so dramatic that you really have nothing new to add; in that case the only respectable thing is to suck it up and move on to another project. Very often, the overlap is noticeable but far from complete, and you still have something interesting to contribute; that turned out to be the case this time. So we soldiered on, giving credit in our paper to those who blazed trails before us, and highlighting those roads which we had traversed all by ourselves.

At the end of the process — from meandering speculation, focusing in on an interesting question, gathering the necessary technical tools, performing the relevant calculation, comparing with the existing literature, and finally writing up the useful results — you have a paper. Considering all the work you have put into it, the actual paper is annoyingly slight as a physical artifact, even if it’s one of the longer ones. Unless you are really lucky (and perhaps also good), the amount of work you really do and stuff you figure out is much more than shows up in the distilled and polished final product. Nevertheless, I always finish the paper-writing process with a feeling of accomplishment and a degree of surprise that it seemed to work yet again.

As often as not, however, the nominal capstone of the process — submitting the paper to the arxiv — is not the final step. There is, of course, the matter of submitting it to a journal and going through the refereeing process, but in this gilded electronic age that’s usually somewhat anticlimactic. No, the real action comes in the couple of days after you’ve put the paper online, in which time you collect helpful emails from your colleagues around the world:

Dear Dr. X:

I enjoyed reading your new paper astro-ph/0701357. You might be interested in the related work I did years ago, astro-ph/yymmnnn.

Warmly, Dr. Y.

Translation: “I want a citation, you bastard.” Although it’s often not at all impolite, and can even be quite helpful — there’s a lot of science out there, and no way for any one person to keep track of it all. Perhaps the most useful feature of the electronic age (as far as scientists go) are the citations services like SPIRES, which put at your fingertips a network of related papers, connected through a web of referencing and being-referenced-by. It’s by no means unreasonable, when one has written a potentially relevant paper, to make some token effort to see that it is included in that network; otherwise it could easily be lost forever. It can be annoying to get too many requests for citations, especially irrelevant ones, but I essentially always go ahead and add them into a revised version of the paper; it doesn’t kill any electrons.

In our case, we didn’t get any of the dreaded emails that point out that someone else had done exactly what our paper had done. There were a couple of confused exchanges back and forth with friends who figured that we must have been motivated by the axis-of-evil stuff, and were trying to convince us that our particular model (with an effect that was scale invariant, rather than concentrated on the largest scales) wasn’t the right way to tackle that problem; we had to explain that we really weren’t trying to solve any sort of pre-existing puzzle, we were just trying to probe the fundamental robustness of the usual assumptions about inflation. In fact, we didn’t go so far in our paper as to actually compare to any CMB data sets — we are possessed of sufficient self-knowledge to understand that there are other people out there much better equipped than we are to carry out such a task. Hopefully it will be carried out soon!

But, although we didn’t get any deal-breaking emails from the outside world, we did get a post-submission insight from the inside world, namely me. As we were writing, there was another thing that had been nibbling at the edges of my consciousness — isn’t there some good reason why inflation usually doesn’t pick out a preferred direction, but rather is completely isotropic? And finally I recalled what it was — something called the Cosmic No-Hair Theorem. This is a result, due to Bob Wald, which essentially says that in a universe filled with positive vacuum energy plus some other stuff, the vacuum energy always wins out. The other stuff always dilutes away, leaving you with the usual isotropic expansion.

Which was interesting, since we had just written a paper featuring a model that did have vacuum energy plus some other (vector) fields, in which the other stuff did not dilute away, but rather imprinted a direction-dependent effect at all scales. Did we goof, or take advantage of a loophole? Happily, it was the latter. In general relativity, you can prove almost nothing without assuming something “reasonable” about the energy-momentum sources, in the form of energy conditions that restrict the energy density and pressure of the stuff you are considering. The cosmic no-hair theorem assumed the Dominant Energy Condition, which is perfectly reasonable; without assuming the DEC, you can’t be sure that your theory is stable.

But our vector fields, it turns out, were more clever than we were. Our theory violates the dominant energy condition, so it is consistent with the results of the theorem. But it is not unstable; if we divide the fields into a homogeneous background plus a set of small perturbations, the background (which is effecting inflation) violates the DEC, but the fluctuations (which would possibly lead to instabilities) actually obey the DEC. So we managed to find a theory that was well-behaved, but which sidestepped the crucial assumption of the cosmic no-hair theorem. That’s why it had been a little tricky to find a good model in which inflation was anisotropic for an extended period; there was a theorem that said it couldn’t happen, and we had to find a clever loophole, even though we didn’t know that’s what we were doing. So we updated the paper to include a few sentences about that situation.

And now, I think, we’re truly done. The paper has been accepted and published and all that. But of course, one good project suggests all sorts of others. If we explored whether the cherished assumption of rotational invariance could be violated during inflation, are there other cherished assumptions we could contemplate violating? Answer: sure, there are plenty. But there are also plenty of unconnected science ideas that are worth pursuing. So we have to decide whether we should continue to move forward with this kind of investigation, or switch to something completely different. (I tend to go with the latter, more often than not.) One of the happy things about being a professional scientist is that there’s no worry that one day you will wake up and all of the good questions will be answered. On to whatever comes next.

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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .

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