A Hemispherical Power Asymmetry from Inflation
Abstract: Measurements of temperature fluctuations by the Wilkinson Microwave Anisotropy Probe (WMAP) indicate that the fluctuation amplitude in one half of the sky differs from the amplitude in the other half. We show that such an asymmetry cannot be generated during single-field slow-roll inflation without violating constraints to the homogeneity of the Universe. In contrast, a multi-field inflationary theory, the curvaton model, can produce this power asymmetry without violating the homogeneity constraint. The mechanism requires the introduction of a large-amplitude superhorizon perturbation to the curvaton field, possibly a pre-inflationary remnant or a superhorizon curvaton-web structure. The model makes several predictions, including non-Gaussianity and modifications to the inflationary consistency relation, that will be tested with forthcoming CMB experiments.
The goal here is to try to explain a curious feature in the cosmic microwave background that has been noted by Hans Kristian Eriksen and collaborators: it’s lopsided. We all (all my friends, anyway) have seen the pretty pictures from the WMAP satellite, showing the 1-part-in-100,000 fluctuations in the temperature of the CMB from place to place in the sky. These fluctuations are understandably a focus of a great deal of contemporary cosmological research, as (1) they arise from density perturbations that grow under the influence of gravity into galaxies and large-scale structure in the universe today, and (2) they appear to be primordial, and may have arisen from a period of inflation in the very early universe. Remarkably, from just a tiny set of parameters we can explain just about everything we observe in the universe on large scales.
The lopsidedness I’m referring to is different from the so-called axis of evil. The latter (in a cosmological context) refers to an apparent alignment of the temperature fluctuations on very large scales, which purportedly pick out a preferred plane in the sky (suspiciously close to the plane of the ecliptic). The lopsidedness is a different effect, in which the overall amplitude of fluctuations is a bit different (just 10% or so) in one direction on the sky than in the other. (A “hemispherical power asymmetry,” if you like.)
What we’re talking about is illustrated in these two simulations kindly provided by Hans Kristian Eriksen.
I know, they look almost the same. But if you peer closely, you will see that the bottom one is the lopsided one — the overall contrast (representing temperature fluctuations) is a bit higher on the left than on the right, while in the untilted image at the top they are (statistically) equal. (The lower image exaggerates the claimed effect in the real universe by a factor of two, just to make it easier to see by eye.)
What could cause such a thing? Our idea was that there was a “supermode” — a fluctuation that varied uniformly across the observable universe, for example if we were sampling a tiny piece of a sinusoidal fluctuation with a wavelength many times the size of our current Hubble radius.
The blue circle is our observable universe, the green curve is the supermode, and the small red squiggles are the local fluctuations that have evolved under the influence of this mode. The point is that the universe is overall just a little bit more dense on one side than the other, so it evolves just slightly differently, and the resulting CMB looks lopsided.
Interestingly, it doesn’t quite work; at least, not in a simple model of inflation driven by a single scalar field. In that case, you can get the power asymmetry, but there is also a substantial temperature anisotropy — the universe is hotter on one side than on the other. There are a few back-and-forth steps in the reasoning that I won’t rehearse here, but at the end of the day you get too much power on very large scales. It’s no fun being a theoretical cosmologist these days, all the data keeps ruling out your good ideas.
But we didn’t give up! It turns out that you can make things work if you have two scalar fields — one that does the inflating, cleverly called the “inflaton,” and the other which is responsible for the density perturbations, which should obviously be called the “perturbon” but for historical reasons is actually called the “curvaton.” By decoupling the source of most of the density in the universe from the source of its perturbations, we have enough wiggle room to make a model that fits the data. But there’s not that much wiggle room, to be honest; we have an allowed region in parameter space that is not too big. That’s good news, as it brings the hope that we can make relatively precise predictions that could be tested by some means other than the CMB.
One interesting feature of this model is that the purported supermode must have originated before the period of inflation that gave rise to the smaller-scale perturbations that we see directly in the CMB. Either it came from earlier inflation, or something entirely pre-inflationary.
So, to make a bit of a segue here, this Wednesday I gave a plenary talk at the summer meeting of the American Astronomical Society in St. Louis. I most discussed the origin of the universe and the arrow of time — I wanted to impress upon people that the origin of the entropy gradient in our everyday environment could be traced back to the Big Bang, and that conventional ideas about inflation did not provide straightforward answers to the problem, and that the Big Bang may not have been the beginning of the universe. I was more interested in stressing that this was a problem we should all be thinking about than pushing any of my favorite answers, but I did mention my paper with Jennie Chen as an example of the kind of thing we should all be looking for.
To an audience of astronomers, talk of baby universes tends to make people nervous, so I wanted to emphasize that (1) it was all very speculative, and (2) even though we don’t currently know how to connect ideas about the multiverse to observable phenomena, there’s no reason to think that it’s impossible in principle, and the whole enterprise really is respectable science. (If only they had all seen my bloggingheads dialogue with John Horgan, I wouldn’t have had to bother.) So I mentioned two different ideas that are currently on the market for ways in which influences of a larger multiverse might show up within our own. One is the idea of colliding bubbles, pursued by Aguirre, Johnson, and Shomer and by Chang, Kleban, and Levi. And the other, of course, was the lopsided-universe idea, since our paper had just appeared the day before. Neither of these possibilities, I was careful to say, applies directly to the arrow-of-time scenario I had just discussed; the point was just that all of these ideas are quite young and ill-formed, and we will have to do quite a bit more work before we can say for sure whether the multiverse is of any help in explaining the arrow of time, and whether we live in the kind of multiverse that might leave observable signatures in our local region. That’s research for you; we don’t know the answers ahead of time.
One of the people in the audience was Chris Lintott, who wrote up a description for the BBC. Admittedly, this is difficult stuff to get all straight the very first time, but I think his article gives the impression that there is a much more direct connection between my arrow-of-time work and our recent paper on the lopsided universe. In particular, there is no necessary connection between the existence of a supermode and the idea that our universe “bubbled off” from a pre-existing spacetime. (There might be a connection, but it is not a necessary one.) If you look through the paper, there’s nothing in there about entropy or the multiverse or any of that; we’re really motivated by trying to explain an interesting feature of the CMB data. Nevertheless, our proposed solution does hint at things that happened before the period of inflation that set up the conditions within our observable patch. These two pieces of research are not of a piece, but they both play a part in a larger story — attempting to understand the low entropy of the early universe suggests the need for something that came before, and it’s good to be reminded that we don’t yet know whether stuff that came before might have left some observable imprint on what we see around us today. Larger stories are what we’re all about.