It's well known that all of our evidence for dark matter (and dark energy, too, but that's not the subject here) at the present time is indirect: It comes from observing the gravitational influence of the hypothetical stuff, not from detecting it "directly" (i.e., using some interaction other than gravitational).

So it's natural to ask whether we can do away with dark matter by positing some modification of the behavior of gravity; I've certainly wondered that myself. And it may very well turn out that the behavior of gravity on large scales does not precisely match the prediction of ordinary general relativity. Nevertheless, I think that, by now, we've accumulated enough data to conclude that the universe cannot be explained solely by modifying gravity; there is ample evidence of gravitational forces pointing in directions where there isn't any (ordinary) "stuff" to create them, leading us to accept the existence of some form of dark matter.

About a year ago I put up a post that explained this point of view, and took aim in particular at the popular framework known as MOND. This led to some good discussion in the comments, and also to a behind-the-scenes email exchange between Rainer Plaga, Stacy McGaugh, and me. It's a bit of old news, but I thought there would still be some interest in our discussion, so (with permission) I'm posting our emails here. Seeing how the sausage is made, as it were. It's a bit of a long read, sorry about that.

Rainer, March 1: Dear Sean, I discussed your recent vigorous defense of CDM your blog with Stacy, and he encouraged me to send you my - absolutely objective ;-) - position. On the one hand I am with you that if Stacy uses terms like "serious fine-tuning problem for LCDM" in his newest paper's abstract (which are then interpreted by science journalists in the way you exhibit), he had to quantitatively compare the expected properties of galaxies under the assumption of LambdaCDM with his data set. If he wants to criticise an idea he has to deal with the idea not with alternatives to it. Alas, he does not do that in this paper. On the other hand I strongly disagree out of principle to require statements like: ?of course we have more than sufficient evidence to conclude that dark matter exists, we?re just trying to understand how it works and what else might be going on.? from anybody. Really Sean, this sounds like a caricature of the holy inquisition to me, "philosophers can speculate as long as they accept that the final truth is already known from the holy scriptures ;-)". Your statement: "Dark matter is real ... there’s no reasonable doubt about the dark matter." is misleading. Stacy and I of course know that dark matter in the form of massive neutrinos does exist beyond reasonable doubt. But that does not answer a crucial question. Crucial questions are: what flattens the rotation curves in galaxies? What creates the third CMB peak? CDM, MOND or something else? In my opinion the final verdict on these questions is not in, yet. Allow me to argue why your top 3 arguments for the existence of CDM do not convince me, perhaps yet. 1. "MOND is ugly": The alternative is not "theory for MOND" vs. GR but "theory for MOND" vs. GR + "theory for CDM particle". The number of exhibited equations then becomes similar. How do you know that TeVeS is uglier than the "theory for CDM particle"? 2. "Clusters require DM anyway" If one could make a case that they require nonbaryonic cold dark matter, I would consider the case settled in favour of CDM. However, the dark matter required for MOND in clusters might be the ca. 40% fraction of baryonic matter that we anyway know is currently missing in clusters (even in LCDM). Do we agree? How can the argument be clinching then? 3. Your strongest argument is the one from the CMB. But still, replacing "MOND" with "CDM", couldn't your statement: "Can some clever theorist tweak things so that there?s a MOND version that actually fits? Probably. Or we could just accept what the data are telling us." be used just as well to comment on the well known problems of CDM to reproduce the detailed properties of galaxies? Wouldn't this be a great topic for another "great debate" a la Shapley/Curtis 1920 between u and Stacy? In that case it turned out both were partly right and wrong, my personal bet: it would be the same this time ;-).

Sean, March 1: Hi Rainer-- Ten years ago, it was perfectly respectable to speculate that there was no such thing as dark matter, just a modification of gravity. (It couldn't have been MOND alone, which was ruled out by clusters, but it could have been some more elaborate modification.) That's no longer true. The Bulltet Cluster and the CMB both provide straightforward evidence that there is gravity pointing in the direction of something other than the ordinary matter. The source for that gravity is "dark matter." It could be simple, like an axion or a thermal relic, or it could be quite baroque, like TeVeS + sprinkles of other dark matter as required, but it's definitely there. If people want to contemplate that there is dark matter and also a modification of gravity, that's fine. If people want to point to features of galaxy/cluster phenomenology and say that these features must be explained, that's absolutely fine. But if people want to cling to the possibility that dark matter doesn't exist, that's not being appropriately cautious, it's just ignoring the data, and it's a disservice to the public to pretend otherwise.

Rainer, March 2: Dear Sean, I do not fully understand your argument: do you argue that the bullet cluster proves that _nonbaryonic_ DM exists? To me Stacy's argument - that MOND might work only with the baryonic cluster DM which is an additional problem even within LCDM - cannot be currently excluded (see 2. in my previous e-mail). Do you disagree with his argument, and if yes, why? For your convenience let me summarize Stacy's general argument in my own words (Stacy please protest if I misrepresent it): a. even within LCDM generally uncontested facts are that in clusters of the size of the bullet cluster (< 10(13) M_sun): 1. ca. 50% of the cluster's _baryonic_ matter is probably in some invisible form 2. the hot gas is a minor component of the total baryonic matter (see e.g. fig.1 here: http://arxiv.org/abs/1007.1980) b. suppose that this baryonic cluster DM is in some non-collisional form (e.g. jupiters). Then a.1. would quantitatively explain MOND's missing cluster DM and a.2. the observational fact that the bullet's cluster mass is concentrated on the galaxies and not the hot gas. It is somewhat paradoxical, but seems clear: if you want to rule out MOND you have to deal with its details, if Stacy wants to rule out CDM he has to deal with its details. Neither of you guys is really doing this, and I can understand why: both of you would feel you are wasting time on a wrong concept. But you would not ;-).

Sean, March 2: Hi Rainer-- We know how much baryonic matter there is from BBN. It's not enough to explain the Bullet Cluster or the CMB, even with MOND. Not to mention that you would have to come up with some way to turn the large majority of baryonic matter into some collisionless form. (The paper you just cited says " the baryons are not missing, they are simply located in cluster outskirts" right there in the abstract.)

Rainer, March 2: Hi Sean,

We know how much baryonic matter there is from BBN. It's not enough to explain the Bullet Cluster or the CMB, even with MOND.

They claim ca. a factor 2 more dark baryonic matter than seen is needed in the clusters. What problem would that pose with BBN? (Don't forget that the baryonic matter/CDM ratios derived from LCDM in clusters are meaningless if MOND were the answer).

Not to mention that you would have to come up with some way to turn the large majority of baryonic matter into some collisionless form.

Yes, this would need some ad-hoc gastrophysics to produce enormous amounts of e.g. jupiters especially in the cluster centre. Not nice, but not impossible, cooling flows etc... But if all that were true, the bullet cluster would be OK.

(The paper you just cited says " the baryons are not missing, they are simply located in cluster outskirts" right there in the abstract.)

But that's exactly what is needed also for MOND: the dark baryons are really hiding somewhere... They are not claiming a detection of these baryons! But let us take a step back on this paper: What it discusses is the fact that clusters need some dark baryonic matter even in LCDM, ca. 30% of the baryonic matter is apparently unseen. This was unexpected, some gastrophysics will be needed to explain it. (They mention "AGN feedack" and stuff...) MOND's problem is more severe, ca. 70% of the baryonic mater would apparently be unseen in the central parts of the clusters. This was unexpected some gastrophysics will be needed to explain it. Sorry, Sean, this seems like an open problem to me both for LCDM and MOND, admittedly a bigger one for MOND (but then clusters are their worst problem...), but not the ultraclean evidence for CDM that you are claiming...

Stacy, March 2: OK, I think at least we all agree that BBN tells us the baryon density of the universe. Lets deal with one thing at a time, the dark matter in clusters. If I understand you, you are saying MOND is falsified because there is dark matter in clusters. Rainer is suggesting that a logical way out of this is if the excess mass in clusters is in some dark, baryonic, collisionless form. I agree it is tough to imagine what that would be (and have consistently said as much) but I am not willing to grant that I know it to be impossible. So the real leap to falsify MOND is to say that the dark mass in clusters is not just dark baryons, but WIMPs (or whatever non-baryonic particles compose CDM). And that follows how? Because Omega_m > Omega_b?

Sean, March 3: MOND without non-baryonic DM is falsified by clusters, because you can't fit them with the baryons implied by BBN regardless of what form they take. That's admitted by most people, e.g. Sanders' paper. More interesting is the question of whether you could get around the need for non-baryonic DM with some other theory of modified gravity. The Bullet Cluster and CMB, again to most people, imply not. Could you wriggle out of that conclusion by combining some new as-yet-unformulated modification of gravity with a huge population of mysterious intergalactic Jupiters? No, because you would still be completely wrong on the CMB. It's time to accept what the data are telling us and move on.

Stacy, March 3:

MOND without non-baryonic DM is falsified by clusters, because you can't fit them with the baryons implied by BBN regardless of what form they take. That's admitted by most people, e.g. Sanders' paper.

Ah. I thought this was the conceptual error you were making. Clusters you certainly could fit just with baryons. They're rare systems. If that is the only place we need dark baryons, then do the integrals. You can satisfy the residual mass discrepancy in clusters in MOND without making much dent in the BBN missing baryon budget. Do I *like* such a solution? Certainly not. Neither do I like that fact that clusters are the only systems that come close to having the right baryon content in LCDM. Whay are galaxies missing more than half of their baryons? Dwarfs > 90%? I can imagine how this might happen, but the solutions are comparably contrived. The more basic point is that I am not willing to condemn a theory for needing some dark baryons if its competitor also needs dark baryons.

More interesting is the question of whether you could get around the need for non-baryonic DM with some other theory of modified gravity. The Bullet Cluster and CMB, again to most people, imply not. Could you wriggle out of that conclusion by combining some new as-yet-unformulated modification of gravity with a huge population of mysterious intergalactic Jupiters? No, because you would still be completely wrong on the CMB. It's time to accept what the data are telling us and move on.

The CMB is really interesting. I correctly predicted the amplitude of the second peak (a prediction that is still quantitatively correct) by making the ansatz that there was whatever generally covariant theory might grow out of MOND looked just like GR in the early universe. Obviously that has to change later in order to grow structure, but at least it gives some proxy for what MOND might do with the CMB. At the time, I discussed some of the ways in which this would inevitably fail. The response initially was that MOND itself made no prediction for the CMB, therefore we should disregard the chance success of this prediction. Now you want to treat the low third peak as an absolute prediction of MOND. You can't have it both ways. Which is it? A low third peak would have falsified LCDM. It survives that test. That does not automatically falisify MOND. It just means that the relativistic parent theory (whatever that might be - it is not obvious to me it has to be TeVeS) has to have a net forcing term a la CDM. Does that seem reasonable to me? No, and (as I said with the ultrafaint dwarfs) I too was ready to write off MOND on this point. But Skordis & Ferreira showed that the scalar field in TeVeS might have just such an effect. So I can not, in good conscience, say it is impossible. You should not accuse me of ignoring data. I have written papers on these subjects. Indeed, one of the things that surprised and impressed me about MOND, when I first got over my initial revulsion and started to look into it, was what a great breadth and wealth of data it did quite in explaining. From the tone of your statements, I imagine you have no idea what I'm talking about. You really ought to check your facts before making ignorant statements to the effect that "MOND only does rotation curves." Indeed, you yourself appear to be ignoring facts. Why do any MOND predictions come true? Let's suppose it is only true that all MOND does is fit rotation curves. That demands an explanation - one you nowhere attempt to provide. Your reasoning appears to boil down to "We're sure that CDM exists, so somehow it must work out." Well, I've tried - very hard - to see how it could work out. It aint easy. I won't say it is impossible. But it is as absurd as some of the above dodges are with MOND. Dark matter in galaxies is like epicycles - you can fit anything you like, but it doesn't explain why a simple formula does better. You may find it hard to believe, but I started from exactly the same perspective as you. I am far more comfortable with CDM than with MOND. I will breathe a great sigh of relief if and when WIMPs are detected in the laboratory. Then we'll know the answer, and we won't have to have these bitter debates. However, I am not being unreasonable in holding the theory to a high standard of proof. If you want to convince me that, for sure, the universe is filled with some till-now hypothetical particle from a hypothetical dark sector outside of the Standard Model of particle physics, then show me a piece. Until then, you are over-reaching.

Sean, March 3: You can't just wave your hands and say that a mysterious "forcing term" will help explain the CMB. If there is no non-baryonic dark matter, there is no way that even-numbered peaks can be different from odd-numbered peaks; the configuration of baryons is precisely analogous. You can mimic the situation in TeVeS (although the numbers don't seem to work out) because you've introduced an independently propagating scalar degree of freedom whose energy density doesn't follow the baryons. You can give that scalar whatever name you like, but it is "non-baryonic dark matter." A particularly contrived version, but that's what it is. You can't explain the third peak without a source for gravity that propagates independently of the baryons.

Rainer, March 3:

MOND without non-baryonic DM is falsified by clusters, because you can't fit them with the baryons implied by BBN regardless of what form they take.

Why is that? I just don't get it, and am very open to be persuaded. 90% of all cosmic baryons are presently undetected, right? Only a fraction of the baryonic matter we see directly is in clusters (O(a few percent), let's say 10%) So why can't a small fraction, say O(2%), of all the cosmic dark baryons be in the form of e.g. jupiters in the central parts of clusters? They and stars would then dominate the cluster mass and be dissipationless ---> no problem with the bullet cluster in MOND.

That's admitted by most people, e.g. Sanders' paper.

Where? In http://arxiv.org/abs/astro-ph/0703590 he states about cluster dark matter in MOND: "For example, there are more than enough undetected baryons to make up the missing dark component; they need only be present in some non-dissipative form which is difficult to observe." He also likes massive neutrinos, but not to the exclusion of baryonic dark matter.

Stacy, March 4: Hi Sean, OK, now we are discussing science again. I take your point about the CMB very seriously. It seems to me that you are putting a lot of weight on the third peak, which is not all THAT well constrained. WMAP really has to scrape to get there, so the result is dominated by the systematics of PSF modeling. I presume they've done that right, but there are double exponential corrections involved in subtracting the foreground and then getting back to the cosmic signal, so they don't have to go far wrong to make a bad mistake with the third peak. Presumably PLANCK will clarify this soon, though a glance at their first release images does not provide a lot of confidence about the foreground MW masks that WMAP used. I also wonder, given the visceral reaction you and others have at any suggestion that LCDM might be questionsed, if the PLANCK team would let themselves admit a low third peak even if the saw it. For now, we have an apparently clear detection of a high third peak in WMAP, and we need to explain the data we have rather than the data we hope soon to have. And honestly, I expect the most likely outcome to be a confirmation of WMAP, with only minor tweaks. So we have to understand the third peak along with clusters and rotation curves and dwarf spheroidals and everything else. I freely admit that I don't know how to make the third peak high. I also don't know that a high-ish thrid peak can't be obtained in a more general theory. I agree with your point that pure baryons shouldn't do that - the vector is wrong, as you say. I'm not even convinced TeVeS can do it. But lots of theories (not just MOND-inspired ones) invoke scalar fields, so I can't exclude the possibility. I also agree that this is contrived. But we are WAY into contrivance with LCDM, a point I believe you've made yourself on occassion. We've just gotten familiar with the contrived parts so that they no longer bother us. That doesn't make them any less contrived. You make the point that the scalar field solution in TeVeS is just a contrived form of non-baryonic dark matter. But even in pure GR we could use some form of non-baryonic dark matter that gives us the MOND phenomenology. Why not consider an effect due to the physical nature of the particles? Until we detect WIMPs, surely you at least agree that we don't really know what the dark matter is? I know everybody invokes feedback to "fix" galaxies, but those models are just as contrived. Actually, they are considerably more contrived, as they inevitably require many more parameters, and those parameters are simply tuned to match observations. Any competent theorist can tune any model to fit a given set of data. I must have said this to you before, but I will say it again. The MOND formula provides an apparently correct description of the effective force law in galaxies. How does the dark matter "know" to arrange itself just so as to look like MOND? If it manages this trick in galaxies, why not in the solar system? How would we know that the solar system isn't really run by an inverse-cube force law, but there is dark matter arranged just so as to make it look like an inverse-square law? Could anything be more contrived?

Sean, March 6: Hi Stacy-- I'm not sure what you are saying about the third peak in the CMB. We agree that "pure baryons shouldn't do that." I can only think of three possibilities. (1) There is some sort of source for gravity other than baryons. (2) There is a modification of gravity that doesn't include new sources, but also doesn't respond directly to where the sources actually are. (3) The data aren't good enough to say that the odd-numbered peaks are boosted relative to what we would expect from damped oscillations of baryons alone. If it's (1), then that's non-baryonic dark matter and we should just admit it. I think that (2) is physically implausible, and as far as I know nobody has suggested otherwise. And I think that the time is past when anyone could credibly hang on to (3). Here's a relatively recent figure (2 years ago) from Ned Wright's web site.

Am I missing a possibility, or would you buy one of these three?

Stacy, March 7: Hi Sean, I basically agree with the 3 possibilities you list. Indeed, I thought that was pretty much what I said. You imply that it is hanging on to vain hope to explain the third peak of the CMB by anything other than a new source. I am saying that it is a vain hope to imagine that turning the crank on any number of CDM numerical simulations is ever going to spit out the observed MONDian phenomenology. Just because LCDM works for the CMB does not automatically guarantee that it'll work in galaxies, any more than MOND's success in galaxies means it must inevitably succeed as a the basis of a cosmological theory. There is a very simple empirical result in the data for galaxies that cosmologists have, by and large, simply ignored. The stated excuse is usually something like "well, galaxies are complicated, non-linear structures" and so we should be excused from explaining them. Indeed, in LCDM galaxies probably should be complicated. But they're not. They're simple. So simple, the obey a single effective force law. Fitting that with dark matter is like fitting epicylces to planetary orbits. Of course you can do it - you have an infinite number of free parameters. But it don't make no sense. I have said for years now that they conclusion you come to depends on how you weigh the evidence. The CMB is an important piece of that evidence. So are rotation curves. It is not obvious to me that the third peak should count 100% and galaxies zero. Yet that is in effect the weighting that lots of people appear to be using.

Sean, March 8: Hi Stacy-- I think we've reached the end of what needs to be said. You agree with my three possibilities, and you agree (I think) that the CMB data are good enough to draw some conclusions. It comes down to whether you are willing to entertain the possibility that there is a mysterious new force that does not involve any new sources, yet also does not respond directly to where the actual sources are. (And in the process reproduces exactly what we would see if there were CDM.) You may think that is plausible -- I, and most people in the field, do not. Therefore, we believe that there is non-baryonic DM, and the question is how it behaves. You seem to think I am defending LCDM, when I have never mentioned it. I am defending the claim that "non-baryonic dark matter exists." As I said in the original post, we certainly have to explain the phenomenology of galaxies and clusters, and the right explanation may very well involve a modification of gravity or interesting new physics in the dark sector -- both of which I've written papers about. Nobody is suggesting that we ignore data from galaxies and clusters. But none of that data straightforwardly implies "non-baryonic dark matter does not exist." It's a complicated dynamical problem. The CMB -- an enormously simpler system, where everything is in the linear regime -- does straightforwardly imply "non-baryonic dark matter exists." Admitting that will improve our chances for future progress.

Stacy, March 8: Yes, we've said what we're going to say. But you still don't seem to get it. The CMB is simple. It is not enormously simpler. Galaxies are also simple. One must invoke absurdly complex mechanisms to make that happen. The argument against dark matter doing this boils down to fine tuning. I don't like fine tuning problems, especially when a theory is not otherwise falsifiable (e.g., epicycles). Note that as you claim not to be specifically defending LCDM, I am not specifically defending MOND. There is an empirical phenomenology that constitutes a fine tuning problem for ANY dark matter picture (that does not some how build it in). Since we can't explicitly falsify the existence of dark matter, what could be worse than this mother of all fine-tuning problems? I understand the implausibility of what you are saying in the CMB, but you seem to miss the same kind of point in galaxies. I worry that we won't find WIMPs and keep pursuing other DM candidates indefinitely - how do we know when to stop? How would this be different from another millenium of dark epicycles?

Rainer, March 18: Dear disputants, Thanks for this really informative and nearly polemic free (Stacy please stop blaming your colleagues to construct epicycles ;-)) debate! To me (and it seems also to Stacy) Sean's concentration on his main argument, makes his case for some kind of "dark non-baryonic field that enters the stress-energy tensor in GR" quite convincing. It then stands to reason (but is not absolutely necessary) to identify it with a quantum field for some new massive particle. If I may make Stacy's main point in my own words: galaxies are observed to be simpler than they would be expected to be: at least a large fraction of them obeys a strange simple MOND rule, which is without a simple plausible motivation in known physics. In addition there are indications that galaxies sometimes behave in ways that they should not in LCDM (tidal dwarves should not contain dark matter but they seem to do). This reminds one of atoms in classical physics, which were expected to show a very complex behaviour but obeyed strange simple rules, sometimes in contradiction to the known physical laws at the time. The old quantum condition comes to mind as somewhat analogous to MOND's law of motion. Initially it was attempted to explain these rules within the known concepts, and that was all right and necessary. But, as quantum mechanics showed, there is _also_ the possibility that strange simple rules for basic objects of the theory are first clues for really new concepts. Sean, don't you have at least a little bit of sympathy for this possibility? I close with following proposal: CDM or MOND? is not a good question. A better question is: are the successes of the MOND rule _perhaps_ a first clue to new concepts which will modify our understanding of the "dark non-baryonic field that enters the stress-energy tensor in GR" in the sense that it is not only a new quantum field within standard QFT?

Sean, March 18: Hi Rainer-- Sure, I'm happy to agree with that. In fact, you will find exactly those sentiments way back in my original blog post on the topic. I just think we're past the point where we can conclude that non-baryonic dark matter exists -- what form it takes, how it interacts, and what additional things might be going on, are all crucially important questions. Of course DM faces important challenges from the phenomenology of complex structures, and that should be taken seriously; but no-DM alternatives are ruled out by the data, which should also be taken seriously.

Stacy, March 19: Science is dead.