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 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.

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Anatomy of a Paper: Part III, CulminationRead More »

In the exciting cliffhanger that was Part One, we saw how the idea behind a paper came to be — nurtured from a meandering speculation into a somewhat well-defined calculational question. In particular, Lotty Ackerman and Mark Wise and I were asking what would happen if there were a preferred direction during inflation — an axis in the sky along which primordial perturbations were just a little bit different than in the perpendicular plane. We guessed, even in the absence of a specific model, that such a statistical anisotropy would show up as a nearly scale-invariant modulation of the power spectrum. Now we need to turn such ideas into something more concrete.

In fact, our phenomenological guess was enough to go and start calculating how this new effect will show up on the CMB, and we all set about doing exactly that. None of us — Mark, Lotty, and I — are really experts at this sort of thing, but that’s why they make books and review articles. (Without Scott Dodelson’s book, I would have been in trouble.) As it turns out, many years ago Mark had written one of the very first papers on deriving CMB anisotropies from inflationary perturbations, so he had a head start on calculating things. But the analysis that he and Larry Abbott had done way back when had concentrated on the gravitational redshift/blueshift of the CMB (the Sachs-Wolfe effect), which is only the most important contribution on large angular scales. Lotty and I realized that we should be able to calculate the effect at every scale all at once, which turned out to be right. It’s true that messy astrophysical effects (acoustic oscillations) become important at medium and small scales, and it would take a real cosmologist to understand them. But all we were doing was changing the initial amplitude of the perturbations, in a direction-dependent way. The eventual effect is simply a product of the initial amplitude and a “transfer function” that encodes the messy fluid dynamics once and for all; since our new primordial power spectrum left the transfer function unaffected, we didn’t have to worry about it.

(More generally, Lotty and I were full contributors when it came to ideas, but Mark is very fast when it comes to calculations. We would have to occasionally distract him with something shiny while we sat down to catch up with the equations.)

So we read up on calculating CMB anisotropies, and applied it to our model. Since everyone usually assumes that all directions are created equal, we couldn’t simply plug and chug; we had to re-do the usual calculations from the start, keeping the extra degree of complexity introduced by our preferred direction. That provided a good excuse to educate ourselves about some of the nitty-gritty involved in turning primordial density perturbations into a signal on the CMB sky. In particular, we had to play with spherical harmonics, which are the conventional way to encode information spread over a sphere — for example, the temperature of the microwave background as a function of position on the sky.

Every good physicist knows the basic properties of spherical harmonics, but we had to do some particular integrals that were not that common. I don’t know about you, but when I’m faced with a nontrivial integral, I try Mathematica first, ask questions later. But Mathematica didn’t know these integrals, so actual work was required. At some point it dawned on me that we could use a recursion equation — relating one spherical harmonic to a set of others — to turn the integral into something doable. No special points for me; my collaborators figured it out independently. Still, it’s always fun to crack a knotty calculational problem.

A few amusing footnotes to the recursion-equation episode. First footnote: I figured it out while sampling a martini at the Hilton Checkers lounge in downtown L.A. This was last fall, while I was still relatively new to the area, and was spending time checking out the various local establishments. Verdict: a pretty good martini, I must say. The bartender was intrigued by all the equations I was happily scribbling, and asked me what was going on. I explained just a bit about the CMB etc., and she was genuinely interested. But then, alas, she mentioned something about astrology. So I had to explain that this was actually very different etc. I got the impression that she ultimately did appreciate the difference between astronomy and astrology, once it was laid right out there. Now if only we could replace the horoscopes in daily newspapers with charts of the night sky.

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Anatomy of a Paper: Part II, CalculationRead More »

How does theoretical physics get done? I had my first exposure to research doing observational astronomy as an undergrad; it was fascinating, following the process all the way from spending freezing nights at the telescope collecting photons, to reducing the data, seeing what the light curves taught you about the stars, to finally writing a paper. But I knew all along that I really wanted to be a theorist. Looking at those papers with their incomprehensible Greek indices filled me with anticipation for the day it would all finally make sense. (Eventually you realize that more and more of it does make sense, but it never all makes sense, or anywhere close. Most of your time is spent thinking about the parts you don’t understand.)

But I had no idea how such papers were actually produced — where did you start? When I was looking at grad schools, I took the train up to Princeton to visit the physics department and knock on people’s doors — rather less planned out than I would advise anyone else to do. (You couldn’t Google people back then.) I found one guy who was sitting in his office, a faint smell of cigar smoke in the background, scribbling equations on a legal pad. Looked promising. I introduced myself and asked a few silly questions, among which was “How do you do research?” He leaned back, propping his sneaker-clad feet onto the desk, fixed me with a look and said “I don’t know. You just have an idea, and then do research about it.” As advice goes, it was more Delphic than practical. I didn’t know at the time that this guy would later be my boss for a while, and eventually win the Nobel Prize.

So I thought it would be fun to describe the process in a bit more detail, using a worked example. It is no exaggeration to say that every paper is different, but there might be some useful lessons in there somewhere. I recently finished a paper with Lotty Ackerman and Mark Wise that is a pretty canonical example — a solid paper, not something earth-shattering that will change the face of science as we know it, but a meaningful contribution with some good ideas and some useful equations. Well, it was “recently finished” when I began writing this monstrously long post, which by now was many months ago. So I’ve decided to divide it into pieces — this will be the first of a three-part series.

Lotty is a grad student here at Caltech; she had previously worked with Mark, who is a respectable particle theorist in the office next to mine. He knew that she was cosmologically inclined, so introduced Lotty and me to each other even before I officially arrived. I suggested to Lotty that we begin to think about density perturbations in inflation (the hypothetical period of accelerated expansion in the early universe), as much because I wanted to learn more about the subject as for any more focused research goal. I’m not the best advisor in the world; I have lots of ideas, but they inevitably start out rather ill-formed, and most of them stay that way. Occasionally one of them coalesces out of the fog into something substantial, and a paper gets written. It’s a harrowing way to operate, especially from the grad-student perspective.

One day Lotty was having lunch with Jonathan Pritchard, another grad student here, and they wondered out loud what would happen if inflation didn’t happen the same way in every direction in space. That is, what the consequences would be if there were some direction picked out throughout the universe, so that inflation occurred at a different rate (or something) parallel to that direction than perpendicular to it. Presumably there would be something different we could observe about the density fluctuations if we looked along that particular direction than if we looked in another direction, but what exactly? How could we tell? And is there some physical mechanism we could imagine introducing that would actually pick out a direction during inflation, and then (just to keep things simple) disappear afterwards so that we wouldn’t notice it today? Don’t ask me why they thought of it. Just the kind of thing you chat about at lunch all the time, if you happen to be a theoretical cosmologist.

This kind of meandering speculation is one way papers get started. You (if you’re like me — I can’t speak for other people) never sit down and say, “Let’s have an idea.” Some people are fortunate enough to have programmatic, focused research agendas — when I was a postdoc at MIT in the early Nineties, Ed Bertschinger had collected around him an amazing set of postdocs and grad students, all focused on understanding temperature anisotropies in the cosmic microwave background and what they could tell us about the universe. It was a great moment to be thinking about those issues, and a lot of those students are now high-powered faculty members with groups of their own. But most theorists are not quite so systematic. You noodle over problems, talk to other people with similar interests (or complementary skill sets), make connections between different ideas. Occasionally a flash of insight will hit just before you fall asleep, or while you’re waiting for the barista to make your latte.

(I should make clear that this particular “What if?” question is not completely unmotivated speculation. Inflation is a great theory, and is likely to be “right” in some yet-to-be-defined sense, but it’s not something that anyone should think we more or less understand. We’re extrapolating well beyond known physics, so it pays to keep an open mind. One way of forcing yourself to keep an open mind is to ask specific and testable questions about the space of possibilities encompassed by your ideas.)

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Anatomy of a Paper: Part I, InspirationRead More »