Note: this is a guest post by David Merritt, following on from his paper on the philosophy of science as applied to aspects of modern cosmology.
Stacy kindly invited me to write a guest post, expanding on some of the arguments in my paper. I’ll start out by saying that I certainly don’t think of my paper as a final word on anything. I see it more like an opening argument — and I say this, because it’s my impression that the issues which it raises have not gotten nearly the attention they deserve from the philosophers of science. It is that community that I was hoping to reach, and that fact dictated much about the content and style of the paper. Of course, I’m delighted if astrophysicists find something interesting there too.
My paper is about epistemology, and in particular, whether the standard cosmological model respects Popper’s criterion of falsifiability — which he argued (quite convincingly) is a necessary condition for a theory to be considered scientific. Now, falsifying a theory requires testing it, and testing it means (i) using the theory to make a prediction, then (ii) checking to see if the prediction is correct. In the case of dark matter, the cleanest way I could think of to do this was via so-called “direct detection”, since the rotation curve of the Milky Way makes a pretty definite prediction about the density of dark matter at the Sun’s location. (Although as I argued, even this is not enough, since the theory says nothing at all about the likelihood that the DM particles will interact with normal matter even if they are present in a detector.)
What about the large-scale evidence for dark matter — things like the power spectrum of density fluctuations, baryon acoustic oscillations, the CMB spectrum etc.? In the spirit of falsification, we can ask what the standard model predicts for these things; and the answer is: it does not make any definite prediction. The reason is that — to predict quantities like these — one needs first to specify the values of a set of additional parameters: things like the mean densities of dark and normal matter; the numbers that determine the spectrum of initial density fluctuations; etc. There are roughly half a dozen such “free parameters”. Cosmologists never even try to use data like these to falsify their theory; their goal is to make the theory work, and they do this by picking the parameter values that optimize the fit between theory and data.
Philosophers of science are quite familiar with this sort of thing, and they have a rule: “You can’t use the data twice.” You can’t use data to adjust the parameters of a theory, and then turn around and claim that those same data support the theory. But this is exactly what cosmologists do when they argue that the existence of a “concordance model” implies that the standard cosmological model is correct. What “concordance” actually shows is that the standard model can be made consistent: i.e. that one does not require different values for the same parameter. Consistency is good, but by itself it is a very weak argument in favor of a theory’s correctness. Furthermore, as Stacy has emphasized, the supposed “concordance” vanishes when you look at the values of the same parameters as they are determined in other, independent ways. The apparent tension in the Hubble constant is just the latest example of this; another, long-standing example is the very different value for the mean baryon density implied by the observed lithium abundance. There are other examples. True “convergence” in the sense understood by the philosophers — confirmation of the value of a single parameter in multiple, independent experiments — is essentially lacking in cosmology.
Now, even though those half-dozen parameters give cosmologists a great deal of freedom to adjust their model and to fit the data, the freedom is not complete. This is because — when adjusting parameters — they fix certain things: what Imre Lakatos called the “hard core” of a research program: the assumptions that a theorist is absolutely unwilling to abandon, come hell or high water. In our case, the “hard core” includes Einstein’s theory of gravity, but it also includes a number of less-obvious things; for instance, the assumption that the dark matter responds to gravity in the same way as any collisionless fluid of normal matter would respond. (The latter assumption is not made in many alternative theories.) Because of the inflexibility of the “hard core”, there are going to be certain parameter values that are also more-or-less fixed by the data. When a cosmologist says “The third peak in the CMB requires dark matter”, what she is really saying is: “Assuming the fixed hard core, I find that any reasonable fit to the data requires the parameter defining the dark-matter density to be significantly greater than zero.” That is a much weaker statement than “Dark matter must exist”. Statements like “We know that dark matter exists” put me in mind of the 18th century chemists who said things like “Based on my combustion experiments, I conclude that phlogiston exists and that it has a negative mass”. We know now that the behavior the chemists were ascribing to the release of phlogiston was actually due to oxidation. But the “hard core” of their theory (“Combustibles contain an inflammable principle which they release upon burning”) forbade them from considering different models. It took Lavoisier’s arguments to finally convince them of the existence of oxygen.
The fact that the current cosmological model has a fixed “hard core” also implies that — in principle — it can be falsified. But, at the risk of being called a cynic, I have little doubt that if a new, falsifying observation should appear, even a very compelling one, the community will respond as it has so often in the past: via a conventionalist stratagem. Pavel Kroupa has a wonderful graphic, reproduced below, that shows just how often predictions of the standard cosmological model have been falsified — a couple of dozen times, according to latest count; and these are only the major instances. Historians and philosophers of science have documented that theories that evolve in this way often end up on the scrap heap. To the extent that my paper is of interest to the astronomical community, I hope that it gets people to thinking about whether the current cosmological model is headed in that direction.