Dark Photons

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.

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74 Responses to Dark Photons

  1. V says:

    If the dark matter particles belong to a hidden sector, then they would also be charged under whatever the hidden sector gauge group happens to be, and so there could be strong interactions between the dark matter particles not just from the U(1). Haven’t such particles already been considered in the hidden sector of string theory models?

  2. Sean says:

    Sure. There’s been a decent amount of work on what would happen if a new short-range force coupled to dark matter, which is what you would tend to get with strong gauge groups (or spontaneously broken ones). The new thing here is a long-range, non-scalar interaction. (Of course the new U(1) symmetry could come from some string or GUT model, which would be another interesting thing to think about.)

  3. From a non-physicist: I don’t feel humbled at all given that the complexity of life has arisen in (what’s the word for?) regular matter. Even if dark matter and dark energy are more complex than expected, surely intelligence can’t develop from them (skipping all the Tao of Physics stuff)?

  4. GP says:

    Robert J Sawyer’s novel Starplex featured some dark biology—planet sized creatures that intentionally shaped galaxies into spirals because they were prettier that way. I’m sure its full of inaccuracies—they communicated via radio, if I remember correctly, which isn’t very dark of them—but an oddball connection to this idea nonetheless!

  5. noname says:

    Hi Sean.

    I have what I hope is a straight forward question. In this model, is dark matter a thermal relic? And if so, shouldn’t you have a corresponding dark CMB? If the dark matter is in thermal equilibrium with regular matter early on, it seems it should be in equilibrium with a dark photon sea, and while the extra degrees of freedom might not be enough to significantly alter BBN, could they alter the epoch of matter-radiation equality, thereby severely distoring the good old CMB?

    Thanks in advance.

  6. Sean says:

    Absolutely, there will be dark background radiation. But the dark sector (dark matter + dark radiation) decouples relatively early on (temperatures of order 10 GeV). After that, energy gets dumped into ordinary photons from other standard-model particles, but not into the dark photons; so soon, the dark temperature is lower than the ordinary temperature. That’s why there is no problem with BBN or the CMB.

  7. Dark light? I’ll believe it when I see it.

  8. TimG says:

    Hi, Sean. I have a basic question. You mentioned that if the density of dark matter is sufficiently low, it won’t annihilate much. But why doesn’t dark matter clump together into higher density objects, the same way ordinary matter clumps together into stars? I mean, the clumping together of ordinary matter is just due to gravity, right? And dark matter feels gravity too.

  9. adonais says:

    Interesting stuff. But the dark-name scheme doesn’t work. I suggest “delectromagnetism” and “phonots.” I hope you can shed some d-light on d-matter. Let there be d-light. Ahem.

  10. Howabout “phonoffs?”

  11. I mean photoff. Whatever.

  12. Sean says:

    TimG– Yes, there will be some annihilations, just as there are for weakly-interacting dark matter particles as dark matter candidates. And our DM will clump, just like non-interacting DM. But, they’re very rare for the parameters that are allowed by galactic dynamics, at the densities we have in real galaxies; in particular, they don’t change the total DM abundance in any significant way.

  13. TimG says:

    And one more question, if you don’t mind: If dark matter turns out to be a superpartner of regular matter, then wouldn’t we expect the corresponding regular matter to also have a “dark charge”?

    In other words, I’m wondering if the idea of a force that only effects dark matter is incompatible with the idea that dark matter has a regular matter superpartner.

  14. TimG says:

    Sean, thanks for your answer to my first question. I guess what I’m really wondering is just how “clumped up” dark matter is in comparison to normal matter.

    Allow me to clarify by telling you a bunch of stuff you of course already know:
    The average density of ordinary matter in the galaxy is pretty low, since the galaxy contains lots of empty space (empty of ordinary matter, at least). But most of that matter finds itself in stars and such where the density is much higher. So the average distance between a typical particle of matter (i.e., one that resides in a star) and its nearest neighbors is much less than you’d get from just looking at the average density of the galaxy as a whole. So it seems to me it’s the density of matter in stars that you’d need to look at to know how likely a typical particle is to get close enough to interact with another particle.

    So when you give a figure like “one dark matter particle per coffee cup sized volume”, are you telling us the average density of dark matter in a typical galaxy, or are you telling us the density in a “star-sized clump” of dark matter? That is, if dark matter even comes in star-sized clumps. If it doesn’t clump up that much but instead is pretty uniformly spread throughout the galaxy, then I’m wondering “How come?” Shouldn’t gravity make dark matter clump up to much the same degree as regular matter?

  15. Serge says:

    Another layman question:
    Are you saying that dark energy, or part of it could be not cosmological constant or scalar field/quintessence, but dark photons instead ? That is the same nature as dark matter.

  16. Jason Dick says:


    No, that doesn’t work. Dark photons would drop off with the expansion of the universe in the exact same way that normal photons do (as the scale factor to the fourth power). Dark energy requires that the energy density be approximately constant with the expansion.

  17. Lab Lemming says:

    “interactions should be sufficiently weak that dark matter particles don’t “cool off” by interacting with each other in galaxies and clusters.”

    If dark matter doesn’t cool off, then how did it get cold enough to stay gravitationally bound in galaxies? Or was in much colder than everything else way back when the Big Bang was still just mediocre sized?

    Also, would dark particle/antiparticle pairs allow black holes to emit dark Hawking radiation? I recommend building a little one at the LHC to experiment on.

  18. Arun says:

    Sorry, should check your paper, but asking here – is the dark charged matter fermionic or bosonic?

  19. ObsessiveMathsFreak says:

    I must confess to being a long term dark matter skeptic, at least when it comes to these kinds of “magic particle” interpretations. We can’t even create or directly examine dark matter, and the only evidence for it comes from cosmological studies which seem _very_ unlikely to provide any information at all about microscale dark matter interactions. I think postulating dark particles and anti-particles, etc, is really stretches this topic into the grossly speculative regions inhabited by the likes of String Theory.

    That said, I am effectively a layman when it comes to cosmological models, so my knowledge of dark matter is only informed by what are essentially popular science materials. Hence my skepticism. I for one would appreciate seeing introductory material, or references to some, that discusses dark matter without fear of presenting concrete equations and models, showing clearly why classical models fail and why dark matter is needed. So far, I have been unable to find any such presentation, not even so much as a basic gravitational model. I think that the lack of such a presentation, passed over in favour much less rigorous ones, is the reason that you see a lot of skepticism on this topic.

    Also, a small point, but I think the physics community may have already been beaten to the dark particle zoo hypothesis by the Fleetmind.

  20. Jason Dick says:

    Lab Lemming,

    Everything cools with the expansion of the universe. This is how dark matter cooled. As long as it’s produced and decoupled from the visible sector early enough, it’s quite cool even before the emission of the CMB. I presume what Sean is talking about with respect to galaxies and clusters is radiative cooling, where the cluster dark matter would lose energy by emitting radiation (in this case, dark photons). And as long as this hypothetical new force is weak enough, that will happen slowly enough that we wouldn’t have yet detected it.

  21. Count Iblis says:

    If the DM in this model also interacts with ordinary matter via the weak interaction, then won’t the DM get an effective ordinary (milli)charge due to radiative corrections, similar to what happens in this case?

  22. Elayne Riggs says:

    I remain convinced that this dark matter fad is something totally created out of thin air (if you’ll pardon the expression) so scientists can make their sums add up, and they’re all going to look very foolish in another few decades…

  23. Xenophage says:

    Have you rediscovered “mirror matter”? The Fine Structure constant is then already installed,


  24. Shantanu says:

    Sean, u probably missed a reply to my earlier comment about Blanchet’s model of dark matter. Is that ruled out by Bullet cluster and would this also have the same dark properties discussed in your paper?