Science

Fred Adams wonders whether we could still have stars if the constants of nature were very different. Answer: very possibly! It’s in arxiv:0807.3697:

Motivated by the possible existence of other universes, with possible variations in the laws of physics, this paper explores the parameter space of fundamental constants that allows for the existence of stars. To make this problem tractable, we develop a semi-analytical stellar structure model that allows for physical understanding of these stars with unconventional parameters, as well as a means to survey the relevant parameter space. In this work, the most important quantities that determine stellar properties — and are allowed to vary — are the gravitational constant $G$, the fine structure constant $alpha$, and a composite parameter $C$ that determines nuclear reaction rates. Working within this model, we delineate the portion of parameter space that allows for the existence of stars. Our main finding is that a sizable fraction of the parameter space (roughly one fourth) provides the values necessary for stellar objects to operate through sustained nuclear fusion. As a result, the set of parameters necessary to support stars are not particularly rare. In addition, we briefly consider the possibility that unconventional stars (e.g., black holes, dark matter stars) play the role filled by stars in our universe and constrain the allowed parameter space.

I’ve never thought that our knowledge of what constituted “intelligent life” was anywhere near good enough to start making statements about the conditions under which it could form, apart from fairly weak stuff like “life probably can’t exist if the universe only lasts for a Planck time.” So when anthropic arguments start to hinge on thinking that fractional changes in the mass of this or that nucleus would result in a universe with no observers, it seems more prudent to admit that we just don’t know. But putting any anthropic considerations aside, it’s still interesting to ask what the universe would look like if the constants of nature were completely different. How robust are the starry skies?

One of the important features of the universe around us is that, on sufficiently large scales, it looks pretty much the same in every direction — “isotropy,” in cosmology lingo. There is no preferred direction to space, in which the universe would look different than in the perpendicular directions. The most compelling evidence for large-scale isotropy comes from the Cosmic Microwave Background (CMB), the leftover radiation from the Big Bang. It’s not perfectly isotropic, of course — there are tiny fluctuations in temperature, which are pretty important; they arise from fluctuations in the density, which grow under the influence of gravity into the galaxies and clusters we see today. Here they are, as measured by the WMAP satellite.

Nevertheless, there is a subtle way for the universe to break isotropy and have a preferred direction: if the tiny observed perturbations somehow have a different character in one direction than in others. The problem is, there are a lot of ways this could happen, and there is a huge amount of data involved with a map of the entire CMB sky. A tiny effect could be lurking there, and be hard to see; or we could see a hint of it, and it would be hard to be sure it wasn’t just a statistical fluke.

In fact, at least three such instances of apparent large-scale anisotropies have been claimed. One is the “axis of evil” — if you look at only the temperature fluctuations on the very largest scales, they seem to be concentrated in a certain plane on the sky. Another is the giant cold spot (or “non-Gaussianity,” if you want to sound like an expert) — the Southern hemisphere seems to have a suspiciously coherent blob of slightly lower than average CMB temperature. And then there is the lopsided universe — the total size of the fluctuations on one half of the sky seems to be slightly larger than on the other half.

All of these purported anomalies in the data, while interesting, are very far from being definitive. Although most people seem to agree that they are features of the data from WMAP, it’s hard to tell whether they are all just statistical flukes, or subtle imperfections in the satellite itself, or contamination by foregrounds (like our own galaxy), or real features of the universe.

Now we seem to have another such anomaly, in which the temperature fluctuations in the CMB aren’t distributed perfectly isotropically across the sky. It comes by way of a new paper by Nicolaas Groeneboom and Hans Kristian Eriksen:

Bayesian analysis of sparse anisotropic universe models and application to the 5-yr WMAP data

Sexy title, eh? Here is the upshot: Groeneboom and Eriksen looked for what experts would call a “quadrupole pattern of statistical anisotropy.” Similar to the lopsided universe effect, where the fluctuations seem to be larger on one side of the sky than the other, this is an “elongated universe” effect — fluctuations are larger along one axis (in both directions) as compared to the perpendicular plane. Here is a representation of the kind of effect we are talking about — not easy to make out, but the fluctuations are supposed to be a bit stronger near the red dots than in the strip in between them.

It’s not a very large signal — “3.8 sigma,” in the jargon of the trade, where 3 sigma basically means “begin to take seriously,” but you might want to get as high as 5 sigma before you say “there definitely seems to be something there.” However, the WMAP data come in different frequencies (V-band and W-band), and the effect seems to be there in both bands. Furthermore, you can look for the effect separately at large angular scales and at small angular scales, and you find it in both cases (with somewhat lower statistical significance, as you might expect). So it’s far from being a gold-plated discovery, but it doesn’t seem to be a complete fluke, either.

Remember, looking for any specific effect is quite a project — there is a lot of data, and the analysis involves manipulating huge matrices, and you have to worry about foregrounds and instrumental effects. So why were these nice folks looking for a power asymmetry along a preferred axis in the sky? Well, you might recall my paper with Lotty Ackerman and Mark Wise, described in the “Anatomy of a Paper” series of blog posts (I, II, III). We were interested in whether the (hypothetical) period of inflation in the early universe might have been anisotropic — expanding just a bit faster in one direction than in the others — and if so, how it would show up in the CMB. What we found was that the natural expectation was a power asymmetry along the preferred axis, and gave a bunch of formulas by which observers could actually look for the effect. That is what Nicolaas and Hans Kristian did, with every expectation that they would establish an upper limit on the size of our predicted effect, which we had labelled g_*. But instead, they found it! The data are saying that

So naturally, Lotty and Mark and I are brushing up on our Swedish in preparation for our upcoming invitations to Stockholm. Okay, not quite. In fact, it’s useful to be very clear about this, given the lessons that were (one hopes) learned in John’s series of posts about Higgs hunting. Namely: small, provocative “signals” such as this happen all the time. It would be completely irresponsible just to take every one of them at face value as telling you something profound about the universe. And the more surprising the result — and this one would be pretty darned surprising — the more skeptical and cautious we have every right to be.

So what are we supposed to think? Certainly not that these guys are just jokers that don’t know how to analyze CMB data; the truth couldn’t be more different. But analyzing data like this is really hard, and other groups will doubtless jump in and do their own analyses, as it should be. It’s certainly possible that there is a small systematic effect in WMAP — “correlated noise” — rather than in the universe. The authors have considered this, of course, and it doesn’t seem to fit the finding very comfortably, but it’s a possibility. The very good news is that the kind of correlated noise one would expect from WMAP (given the pattern it used to scan across the sky) is completely different from that the we would worry about from the upcoming Planck mission, scheduled to launch next year.

Or, of course, we could be learning something deep about the universe. Maybe even that inflation was anisotropic, as Lotty and Mark and I contemplated. Or, perhaps more plausibly, there is some single real effect in the universe that is conspiring to give us all of the tantalizing hints contained in the various anomalies listed above. We don’t know yet. That’s what makes it fun.

Here’s a new paper of mine, with Adrienne Erickcek and Mark Kamionkowski:

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.