Category: Science

The title is a bit misleading; what is being referred to is not a realistic cosmological model at all. But it’s interesting to see that not every professional astronomer believes in the Big Bang model; there are still some out there who are sticking with the Steady State theory. Seriously.

A Realistic Cosmological Model Based on Observations and Some Theory Developed Over the Last 90 Years
Authors: Geoffrey Burbidge

Abstract: This meeting is entitled “A Century of Cosmology.” But most of the papers being given here are based on work done very recently and there is really no attempt being made to critically review what has taken place in the last 90 or 100 years. Instead, in general the participants accept without question that cosmology equates to “hot big bang cosmology” with all of its bells and whistles. All of the theory and the results obtained from observations are interpreted on the assumption that this extremely popular model is the correct one, and observers feel that they have to interpret its results in terms of what this theory allows. No one is attempting to seriously test the model with a view to accepting it or ruling it out. They are aware, as are the theorists, that there are enough free parameters available to fix up almost any model of the type.

The current scheme given in detail for example by Spergel et al (206, 2007) demonstrates this. How we got to this stage is never discussed, and little or no attention is paid to the observations obtained since the 1960s on activity in the centers of galaxies and what they imply. We shall show that they are an integral part of a realistic cosmological model. In this paper I shall take a different approach, showing first how cosmological ideas have developed over the last 90 years and where mistakes have been made. I shall conclude with a realistic model in which all of the observational material is included, and compare it with the popular model. Not surprisingly I shall show that there remain many unsolved problems, and previously unexpected observations, most of which are ignored or neglected by current observers and theorists, who believe that the hot big bang model must be correct.

For those with any lingering doubts, the Big Bang model — the idea that the universe has evolved from a hot, dense, smooth initial state — is correct, and the Steady State model should have been put to bed a long time ago. Evidence for the Big Bang is overwhelming. It’s a model that keeps making predictions, which keep turning out to be correct, while the Steady State theory made many predictions that turned out to be wrong.

But it’s an interesting case study in how science works. Reading Burbidge’s paper, the parallels with anti-evolutionists are striking. In both cases, one is repeatedly told that the establishment’s supporter’s can’t prove that their theory is correct. Which is undeniably true, as science never proves anything; it just accumulates evidence, and in the case of the Big Bang and natural selection, the evidence puts the case beyond reasonable doubt. Which doesn’t imply that there are no interesting questions remaining to be addressed. For both the Big Bang and natural selection, many of the details concerning the way in which the broad framework is specifically implemented in the real world remain to be answered. And in both cases, the skeptics like to pretend that open questions about the details are the same as open questions about the framework. But they’re not.

Nevertheless, one of the virtues of the tenure system is that a Big Bang skeptic can keep their position as a professor of physics, writing heterodox articles and submitting them to the arxiv. And this really is a virtue, not a flaw. Geoffrey Burbidge has done lots of respectable work in observational astronomy. Long ago, he and his wife Margaret collaborated with Fred Hoyle and Willy Fowler on an important paper that helped established the theory of nucleosynthesis in stars. Part of the motivation for the paper was the realization that conditions in the Big Bang were not right for synthesizing elements much heavier than lithium — you could explain the universe’s helium abundance, but not the existence of carbon and iron and so forth. Hoyle, of course, was one of the originators of the Steady State theory, and that was certainly part of his motivation at the time. As it turns out, in the real world, some elements are synthesized in the early universe, and some in stars, and some in supernovae; the real world can be a messy place.

Would a young cosmologist who didn’t believe in the Big Bang be offered a faculty job, or receive tenure, today? Probably not. Faculty jobs are scarce commodities, and a university is going to want to hire people who will do interesting and productive work that is of some use to the wider community. Believers in the Steady State model aren’t going to produce such work, any more than creationists or astrologers or experts in the plum-pudding model of the atom. And eventually support for the model will fade away entirely, opening the door for the next generation of heterodoxies.

Cosmologists find themselves in this interesting situation where they have a set of hypotheses — dark matter, dark energy, inflation — that serve to make impressively precise predictions that have been tested against a wide variety of data, but presently lack a firm grounding in established physics. We don’t know what exactly the dark matter is, what the dark energy is, or how inflation happened, if indeed it happened at all. So it behooves us to push at the boundaries a bit — start with the simple models and tweak them in some way, and then check whether the new version still fits the data. How confident are we that the dark sector has the properties we think it does, or that inflation happened in a straightforward way?

This was the philosophy that led Lotty Ackerman, Mark Wise and I to ask what the universe would look like if rotational invariance were violated during inflation — if there were a preferred direction in space, which left some imprint on the cosmological perturbations that currently show up as large-scale structure and temperature fluctuations in the cosmic microwave background. I talked about how that paper came to be in a series of posts: one, two, three. And now there is even tantalizing evidence that our model fits the data! I don’t get too excited about it, but it’s something to keep an eye on as the data improve (e.g. when the Planck satellite gets results).

Ever since then, Mark and I have toyed with the idea that once you’ve broken rotational invariance, your next step is obvious: violate translational invariance! Instead of imagining a preferred direction in space, imagine there were a preferred place in the universe. Not because you have some good reason to think there is, but because you want to quantify the level of confidence we have in the assumption that there is not.

So we have now teamed up with Chien-Yao Tseng, another grad student here at Caltech, to do exactly that. The result is this paper:

Translational Invariance and the Anisotropy of the Cosmic Microwave Background
Sean M. Carroll, Chien-Yao Tseng and Mark B. Wise

Primordial quantum fluctuations produced by inflation are conventionally assumed to be statistically homogeneous, a consequence of translational invariance. In this paper we quantify the potentially observable effects of a small violation of translational invariance during inflation, as characterized by the presence of a preferred point, line, or plane. We explore the imprint such a violation would leave on the cosmic microwave background anisotropy, and provide explicit formulas for the expected amplitudes $langle a_{lm}a_{l’m’}^*rangle$ of the spherical-harmonic coefficients.

It took a while to put into equations what exactly was meant by “violating translational invariance” in an operational way. But once you figure it out, it’s obvious, and there are three ways to do it: imagining that there is a preferred point, line, or plane in the universe. Then you hypothesize that the density fluctuations are very slightly modulated in a way that depends on your distance from that preferred place. Once you have that, it’s just a matter of cranking out some monstrous equations. Thank goodness there are only three macroscopic dimensions of space, is all I can say.

So now we have some predictions to compare with data, so that we can understand exactly how well the cosmic microwave background really assures us that there is no special place in the universe. But aside from the general motivation of being careful to test all of our cherished assumptions, there is another reason for work like this: there are a handful of ways in which cosmological perturbations don’t look completely the same in every direction. As we say in the paper:

There is another important motivation for studying deviations from pure statistical isotropy of cosmological perturbations: a number of analyses have found evidence that such deviations might exist in the real world. These include the “axis of evil” alignment of low multipoles, the existence of an anomalous cold spot in the CMB, an anomalous dipole power asymmetry, a claimed “dark flow” of galaxy clusters measured by the Sunyaev-Zeldovich effect, as well as a possible detection of a quadrupole power asymmetry of the type predicted by ACW in the WMAP five-year data. In none of these cases is it beyond a reasonable doubt that the effect is more than a statistical fluctuation, or an unknown systematic effect; nevertheless, the combination of all of them is suggestive. It is possible that statistical isotropy/homogeneity is violated at very high significance in some specific fashion that does not correspond precisely to any of the particular observational effects that have been searched for, but that would stand out dramatically in a better-targeted analysis.

In other words, we have a handful of anomalies, each of which might easily go away, but perhaps when they are taken together they imply that something is going on. Maybe there is some incredibly strong signal out there, and we just haven’t been looking for it in the right way. We won’t know until we understand better how such anomalies would show up in the observations — and then go collect better data.

It’s humbling to think that ordinary matter, including all of the elementary particles we’ve ever detected in laboratory experiments, only makes up about 5% of the energy density of the universe. The rest, of course, comes in the form of a dark sector: some form of energy density that can be reliably inferred through the gravitational fields it creates, but which we haven’t been able to make or touch directly ourselves.

It’s irresistible to imagine that the dark sector might be interesting. In other words, thinking like a physicist, it’s natural to wonder whether the dark sector might be complicated, with a rich phenomenology all its own. And in fact there is something interesting going on: over the last 15 years we’ve established that the dark sector comes in at least two different pieces! There is dark matter, 25% of the universe, which we know is like “matter” because it behaves that way — in particular, it clumps together under the force of gravity, and its energy density dilutes away as the universe expands. And then there is dark energy, 70% of the universe, which seems to be eerily uniform — smoothly distributed through space, and persistent (non-diluting) through time. So, there is at least that much structure in the dark sector.

But so far, there’s no evidence of anything interesting beyond that. Indeed, the individual components of dark matter and dark energy seem relatively vanilla and featureless; more precisely, taking them to be “minimal” provides an extremely good fit to the data. For dark matter, “minimal” means that the particles are cold (slowly moving) and basically non-interacting with each other. For dark energy, “minimal” means that it is perfectly constant throughout space and time — a pure vacuum energy, rather than something more lively.

Still — all we have are upper limits, not firm conclusions. It’s certainly possible that there is a bushel of interesting physics going on in the dark sector, but it’s just too subtle for us to have noticed yet. So it’s important for we theorists to propose specific, testable models of non-minimal dark sectors, so that observers have targets to shoot for when we try to constrain just how interesting the darkness really is.

Along those lines, Lotty Ackerman, Matt Buckley, Marc Kamionkowski and I have just submitted a paper that explores what I think is a particularly provocative possibility: that, just like ordinary matter couples to a long-range force known as “electromagnetism” mediated by particles called “photons,” dark matter couples to a new long-range force known (henceforth) as “dark electromagnetism,” mediated by particles known (from now on) as “dark photons.”

Dark Matter and Dark Radiation
Authors: Lotty Ackerman, Matthew R. Buckley, Sean M. Carroll, Marc Kamionkowski

We explore the feasibility and astrophysical consequences of a new long-range U(1) gauge field (“dark electromagnetism”) that couples only to dark matter, not to the Standard Model. The dark matter consists of an equal number of positive and negative charges under the new force, but annihilations are suppressed if the dark matter mass is sufficiently high and the dark fine-structure constant $hatalpha$ is sufficiently small. The correct relic abundance can be obtained if the dark matter also couples to the conventional weak interactions, and we verify that this is consistent with particle-physics constraints. The primary limit on $hatalpha$ comes from the demand that the dark matter be effectively collisionless in galactic dynamics, which implies $hatalpha$ < 10^-3 for TeV-scale dark matter. These values are easily compatible with constraints from structure formation and primordial nucleosynthesis. We raise the prospect of interesting new plasma effects in dark matter dynamics, which remain to be explored.

Just to translate that a bit, here is the idea. We’re imagining there is a completely new kind of photon, which couples to dark matter but not to ordinary matter. So there can be dark electric fields, dark magnetic fields, dark radiation, etc. The dark matter itself consists half of particles with dark charge +1, and half with antiparticles with dark charge -1. Now you might say to yourself, “Why don’t the particles and antiparticles all just annihilate into dark photons?” That kind of thinking is probably why ideas like this weren’t explored twenty years ago (as far as we know). But if you think about it, there is clearly a range of possibilities for which the dark matter doesn’t annihilate very efficiently; for example, if the mass of the individual dark matter particles was sufficiently large, their density would be very low, and they just wouldn’t ever bump into each other. Alternatively, if the strength of the new force was extremely weak, it just wouldn’t be that effective in bringing particles and antiparticles together.

None of that is surprising; the interesting bit is that when you run the numbers, they turn out to be pretty darn reasonable, as far as particle physics is concerned. For DM particles weighing several hundred times the mass of the proton, there should be about one DM particle per coffee-cup-sized volume of space. The strength of the dark electromagnetic force is characterized, naturally, by the dark fine-structure constant; remember that ordinary electromagnetism is characterized by the ordinary fine-structure constant α = 1/137. It turns out that the upper limit on the dark fine-structure constant required to stop the dark matter particles from annihilating away is — about the same! I was expecting it to be 10^-15 or something like that, and it was remarkable that such large values were allowed.

However, we know a little more about the dark matter than “it doesn’t annhilate.” We also know that it is close to collisionless — dark matter particles don’t bump into each other very often. If they did, all sorts of things would happen to the shape of galaxies and clusters that we don’t actually observe. So there is another limit on the strength of dark electromagnetism: interactions should be sufficiently weak that dark matter particles don’t “cool off” by interacting with each other in galaxies and clusters. That turns into a more stringent bound on the dark fine-structure constant: about an order of magnitude smaller, at $hatalpha$ < 10^-3. Still, not so bad.

More interestingly, we can’t say with perfect confidence that the dark matter really is effectively non-interacting. If a model like ours is right, and the strength of dark electromagnetism is near the upper bound of its allowed value, there might be very important consequences for the evolution of large-scale structure. At the moment, it’s a little bit hard to figure out what those consequences actually are, for mundane calculational reasons. What we are proposing is that the dark matter is really a plasma, and to understand how structure forms, one needs to consider dark magnetohydrodynamics. That’s a non-trivial task, but we’re hoping it will keep a generation of graduate students cheerfully occupied.

The idea of new forces acting on dark matter is by no means new; I’ve worked on it recently myself, and so have certain co-bloggers. (Strong, silent types who are too proud to blog about their own papers.) What’s exciting about dark photons is that they are much more natural from a particle-physics perspective. Typical models of quintessence and long-range fifth forces invoke scalar fields, which are easy and fun to work with, but which by all rights should have huge masses, and therefore not be very long-range at all. The dark photon comes from a gauge symmetry, just like the ordinary photon, and its masslessness is therefore completely natural.

Even the dark photon is not new. In a recent paper, Feng, Tu, and Yu proposed not just dark photons, but a barrelful of new dark fields and interactions:

Thermal Relics in Hidden Sectors
Authors: Jonathan L. Feng, Huitzu Tu, Hai-Bo Yu

Dark matter may be hidden, with no standard model gauge interactions. At the same time, in WIMPless models with hidden matter masses proportional to hidden gauge couplings squared, the hidden dark matter’s thermal relic density may naturally be in the right range, preserving the key quantitative virtue of WIMPs. We consider this possibility in detail. We first determine model-independent constraints on hidden sectors from Big Bang nucleosynthesis and the cosmic microwave background. Contrary to conventional wisdom, large hidden sectors are easily accommodated…

They show that these models manage to evade all sorts of limits you might be worried about, from getting the right relic abundance to fitting in with constraints from primordial nucleosynthesis and the cosmic microwave background.

Our model is actually simpler, because we have a different flavor of fish to fry: the possible impacts of this new long-range force in the dark sector on observable cosmological dynamics. We’re not sure yet what all of those impacts are, but they are fun to contemplate. And of course, another difference between dark electromagnetism and a boring scalar force is that electromagnetism has both positive and negative charges — thus, both attractive and repulsive forces. (Scalar forces tend to be simply attractive, and get all mixed up with gravity.) So we can imagine much more than a single species of dark matter; what if you had two different types of stable particles that carried dark charge? Then we’d be able to make dark atoms, and could start writing papers on dark chemistry.

You know that dark biology is not far behind. Someday perhaps we’ll be exchanging signals with the dark internet.