Cepheids & Gaia: No Systematic in the Hubble Constant

Cepheids & Gaia: No Systematic in the Hubble Constant

Casertano et al. have used Gaia to provide a small but important update in the debate over the value of the Hubble Constant. The ESA Gaia mission is measuring parallaxes for billions of stars. This is fundamental data that will advance astronomy in many ways, no doubt settling long standing problems but also raising new ones – or complicating existing ones.

Traditional measurements of the H0 are built on the distance scale ladder, in which distances to nearby objects are used to bootstrap outwards to more distant ones. This works, but is also an invitation to the propagation of error. A mistake in the first step affects all others. This is a long-standing problem that informs the assumption that the tension between H0 = 67 km/s/Mpc from Planck and H0 = 73 km/s/Mpc from local measurements will be resolved by some systematic error – presumably in the calibration of the distance ladder.

Well, not so far. Gaia has now measured enough Cepheids in our own Milky Way to test the calibration used to measure the distances of external galaxies via Cepheids. This was one of the shaky steps where things seemed most likely to go off. But no – the scales are consistent at the 0.3% level. For now, direct measurement of the expansion rate remains H0 = 73 km/s/Mpc.

Critical Examination of the Impossible

Critical Examination of the Impossible

It has been proposal season for the Hubble Space Telescope, so many astronomers have been busy with that. I am no exception. Talking to others, it is clear that there remain many more excellent Hubble projects than available observing time.

So I haven’t written here for a bit, and I have other tasks to get on with. I did get requests for a report on the last conference I went to, Beyond WIMPs: from Theory to Detection. They have posted video from the talks, so anyone who is interested may watch.

I think this is the worst talk I’ve given in 20 years. Maybe more. Made the classic mistake of trying to give the talk the organizers asked for rather than the one I wanted to give. Conference organizers mean well, but they usually only have a vague idea of what they imagine you’ll say. You should always ignore that and say what you think is important.

When speaking or writing, there are three rules: audience, audience, audience. I was unclear what the audience would be when I wrote the talk, and it turns out there were at least four identifiably distinct audiences in attendance. There were skeptics – particle physicists who were concerned with the state of their field and that of cosmology, there were the faithful – particle physicists who were not in the least concerned about this state of affairs, there were the innocent – grad students with little to no background in astronomy, and there were experts – astroparticle physicists who have a deep but rather narrow knowledge of relevant astronomical data. I don’t think it would have been possible to address the assigned topic (a “Critical Examination of the Existence of Dark Matter“) in a way that satisfied all of these distinct audiences, and certainly not in the time allotted (or even in an entire semester).

It is tempting to give an interruption by interruption breakdown of the sociology, but you may judge that for yourselves. The one thing I got right was what I said at the outset: Attitude Matters. You can see that on display throughout.

This comic has been hanging on a colleague’s door for decades.

In science as in all matters, if you come to a problem sure that you already know the answer, you will leave with that conviction. No data nor argument will shake your faith. Only you can open your own mind.

Cosmology and Convention (continued)

Cosmology and Convention (continued)
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.

Fig. 14 from Kroupa (2012) quantifying setbacks to the Standard Model of Cosmology (SMoC).



Hubble constant redux

Hubble constant redux

There is a new article in Science on the expansion rate of the universe, very much along the lines of my recent post. It is a good read that I recommend. It includes some of the human elements that influence the science.

When I started this blog, I recalled my experience in the ’80s moving from a theory-infused institution to a more observationally and empirically oriented one. At that time, the theory-infused cosmologists assured us that Sandage had to be correct: H0 = 50. As a young student, I bought into this. Big time. I had no reason not to; I was very certain of the transmitted lore. The reasons to believe it then seemed every bit as convincing a the reasons to believe ΛCDM today. When I encountered people actually making the measurement, like Greg Bothun, they said “looks to be about 80.”

This caused me a lot of cognitive dissonance. This couldn’t be true. The universe would be too young (at most ∼12 Gyr) to contain the oldest stars (thought to be ∼18 Gyr at that time). Worse, there was no way to reconcile this with Inflation, which demanded Ωm = 1. The large deceleration of the expansion caused by high Ωm greatly exacerbated the age problem (only ∼8 Gyr accounting for deceleration). Reconciling the age problem with Ωm = 1 was hard enough without raising the Hubble constant.

Presented with this dissonant information, I did what most of us humans do: I ignored it. Some of my first work involved computing the luminosity function of quasars. With the huge distance scale of H0 = 50, I remember noticing how more distant quasars got progressively brighter. By a lot. Yes, they’re the most luminous things in the early universe. But they weren’t just outshining a galaxy’s worth of stars; they were outshining a galaxy of galaxies.

That was a clue that the metric I was assuming was very wrong. And indeed, since that time, every number of cosmological significance that I was assured in confident tones by Great Men that I Had to Believe has changed by far more than its formal uncertainty. In struggling with this, I’ve learned not to be so presumptuous in my beliefs. The universe is there for us to explore and discover. We inevitably err when we try to dictate how it Must Be.

The amplitude of the discrepancy in the Hubble constant is smaller now, but the same attitudes are playing out. Individual attitudes vary, of course, but there are many in the cosmological community who take the attitude that the Planck data give H0 = 67.8 so that is the right number. All other data are irrelevant; or at best flawed until brought into concordance with the right number.

It is Known, Khaleesi. 

Often these are the same people who assured us we had to believe Ωm = 1 and H0 = 50 back in the day. This continues the tradition of arrogance about how things must be. This attitude remains rampant in cosmology, and is subsumed by new generations of students just as it was by me. They’re very certain of the transmitted lore. I’ve even been trolled by some who seem particularly eager to repeat the mistakes of the past.

From hard experience, I would advocate a little humility. Yes, Virginia, there is a real tension in the Hubble constant. And yes, it remains quite possible that essential elements of our cosmology may prove to be wrong. I personally have no doubt about the empirical pillars of the Big Bang – cosmic expansion, Big Bang Nucleosynthesis, and the primordial nature of the Cosmic Microwave Background. But Dark Matter and Dark Energy may well turn out to be mere proxies for some deeper cosmic truth. IF that is so, we will never recognize it if we proceed with the attitude that LCDM is Known, Khaleesi.

Neutrinos got mass!

Neutrinos got mass!

In 1984, I heard Hans Bethe give a talk in which he suggested the dark matter might be neutrinos. This sounded outlandish – from what I had just been taught about the Standard Model, neutrinos were massless. Worse, I had been given the clear impression that it would screw everything up if they did have mass. This was the pervasive attitude, even though the solar neutrino problem was known at the time. This did not compute! so many of us were inclined to ignore it. But, I thought, in the unlikely event it turned out that neutrinos did have mass, surely that would be the answer to the dark matter problem.

Flash forward a few decades, and sure enough, neutrinos do have mass. Oscillations between flavors of neutrinos have been observed in both solar and atmospheric neutrinos. This implies non-zero mass eigenstates. We don’t yet know the absolute value of the neutrino mass, but the oscillations do constrain the separation between mass states (Δmν,212 = 7.53×10−5 eV2 for solar neutrinos, and Δmν,312 = 2.44×10−3 eV2 for atmospheric neutrinos).

Though the absolute values of the neutrino mass eigenstates are not yet known, there are upper limits. These don’t allow enough mass to explain the cosmological missing mass problem. The relic density of neutrinos is

Ωνh2 = ∑mν/(93.5 eV)

In order to make up the dark matter density (Ω ≈ 1/4), we need ∑mν ≈ 12 eV. The experimental upper limit on the electron neutrino mass is mν < 2 eV. There are three neutrino mass eigenstates, and the difference in mass between them is tiny, so ∑mν < 6 eV. Neutrinos could conceivably add up to more mass than baryons, but they cannot add up to be the dark matter.

In recent years, I have started to hear the assertion that we have already detected dark matter, with neutrinos given as the example. They are particles with mass that only interact with us through the weak nuclear force and gravity. In this respect, they are like WIMPs.

Here the equivalence ends. Neutrinos are Standard Model particles that have been known for decades. WIMPs are hypothetical particles that reside in a hypothetical supersymmetric sector beyond the Standard Model. Conflating the two to imply that WIMPs are just as natural as neutrinos is a false equivalency.

That said, massive neutrinos might be one of the few ways in which hierarchical cosmogony, as we currently understand it, is falsifiable. Whatever the dark matter is, we need it to be dynamically cold. This property is necessary for it to clump into dark matter halos that seed galaxy formation. Too much hot (relativistic) dark matter (neutrinos) suppresses structure formation. A nascent dark matter halo is nary a speed bump to a neutrino moving near the speed of light: if those fast neutrinos carry too much mass, they erase structure before it can form.

One of the great successes of ΛCDM is its explanation of structure formation: the growth of large scale structure from the small fluctuations in the density field at early times. This is usually quantified by the power spectrum – in the CMB at z > 1000 and from the spatial distribution of galaxies at z = 0. This all works well provided the dominant dark mass is dynamically cold, and there isn’t too much hot dark matter fighting it.

The power spectrum from the CMB (low frequency/large scales) and the galaxy distribution (high frequency/”small” scales). Adapted from Whittle.

How much is too much? The power spectrum puts strong limits on the amount of hot dark matter that is tolerable. The upper limit is ∑mν < 0.12 eV. This is an order of magnitude stronger than direct experimental constraints.

Usually, it is assumed that the experimental limit will eventually come down to the structure formation limit. That does seem likely, but it is also conceivable that the neutrino mass has some intermediate value, say mν ≈ 1 eV. Such a result, were it to be obtained experimentally, would falsify the current CDM cosmogony.

Such a result seems unlikely, of course. Shooting for a narrow window such as the gap between the current cosmological and experimental limits is like drawing to an inside straight. It can happen, but it is unwise to bet the farm on it.

It should be noted that a circa 1 eV neutrino would have some desirable properties in an MONDian universe. MOND can form large scale structure, much like CDM, but it does so faster. This is good for clearing out the voids and getting structure in place early, but it tends to overproduce structure by z = 0. An admixture of neutrinos might help with that. A neutrino with an appreciable mass would also help with the residual mass discrepancy MOND suffers in clusters of galaxies.

If experiments measure a neutrino mass in excess of the cosmological limit, it would be powerful motivation to consider MOND-like theories as a driver of structure formation. If instead the neutrino does prove to be tiny, ΛCDM will have survived another test. That wouldn’t falsify MOND (or really have any bearing on it), but it would remove one potential “out” for the galaxy cluster problem.

Tiny though they be, neutrinos got mass! And it matters!

LCDM has met the enemy, and it is itself

LCDM has met the enemy, and it is itself

David Merritt recently published the article “Cosmology and convention” in Studies in History and Philosophy of Science. This article is remarkable in many respects. For starters, it is rare that a practicing scientist reads a paper on the philosophy of science, much less publishes one in a philosophy journal.

I was initially loathe to start reading this article, frankly for fear of boredom: me reading about cosmology and the philosophy of science is like coals to Newcastle. I could not have been more wrong. It is a genuine page turner that should be read by everyone interested in cosmology.

I have struggled for a long time with whether dark matter constitutes a falsifiable scientific hypothesis. It straddles the border: specific dark matter candidates (e.g., WIMPs) are confirmable – a laboratory detection is both possible and plausible – but the concept of dark matter can never be excluded. If we fail to find WIMPs in the range of mass-cross section parameters space where we expected them, we can change the prediction. This moving of the goal post has already happened repeatedly.

The cross-section vs. mass parameter space for WIMPs. The original, “natural” weak interaction cross-section (10-39) was excluded long ago, as were early attempts to map out the theoretically expected parameter space (upper pink region). Later predictions drifted to progressively lower cross-sections. These evaded experimental limits at the time, and confident predictions were made that the dark matter would be found.  More recent data show otherwise: the gray region is excluded by PandaX (2016). [This plot was generated with the help of DMTools hosted at Brown.]
I do not find it encouraging that the goal posts keep moving. This raises the question, how far can we go? Arbitrarily low cross-sections can be extracted from theory if we work at it hard enough. How hard should we work? That is, what criteria do we set whereby we decide the WIMP hypothesis is mistaken?

There has to be some criterion by which we would consider the WIMP hypothesis to be falsified. Without such a criterion, it does not satisfy the strictest definition of a scientific hypothesis. If at some point we fail to find WIMPs and are dissatisfied with the theoretical fine-tuning required to keep them hidden, we are free to invent some other dark matter candidate. No WIMPs? Must be axions. Not axions? Would you believe light dark matter? [Worst. Name. Ever.] And so on, ad infinitum. The concept of dark matter is not falsifiable, even if specific dark matter candidates are subject to being made to seem very unlikely (e.g., brown dwarfs).

Faced with this situation, we can consult the philosophy science. Merritt discusses how many of the essential tenets of modern cosmology follow from what Popper would term “conventionalist stratagems” – ways to dodge serious consideration that a treasured theory is threatened. I find this a compelling terminology, as it formalizes an attitude I have witnessed among scientists, especially cosmologists, many times. It was put more colloquially by J.K. Galbraith:

“Faced with the choice between changing one’s mind and proving that there is no need to do so, almost everybody gets busy on the proof.”

Boiled down (Keuth 2005), the conventionalist strategems Popper identifies are

  1. ad hoc hypotheses
  2. modification of ostensive definitions
  3. doubting the reliability of the experimenter
  4. doubting the acumen of the theorist

These are stratagems to be avoided according to Popper. At the least they are pitfalls to be aware of, but as Merritt discusses, modern cosmology has marched down exactly this path, doing each of these in turn.

The ad hoc hypotheses of ΛCDM are of course Λ and CDM. Faced with the observation of a metric that cannot be reconciled with the prior expectation of a decelerating expansion rate, we re-invoke Einstein’s greatest blunder, Λ. We even generalize the notion and give it a fancy new name, dark energy, which has the convenient property that it can fit any observed set of monotonic distance-redshift pairs. Faced with an excess of gravitational attraction over what can be explained by normal matter, we invoke non-baryonic dark matter: some novel form of mass that has no place in the standard model of particle physics, has yet to show any hint of itself in the laboratory, and cannot be decisively excluded by experiment.

We didn’t accept these ad hoc add-ons easily or overnight. Persuasive astronomical evidence drove us there, but all these data really show is that something dire is wrong: General Relativity plus known standard model particles cannot explain the universe. Λ and CDM are more a first guess than a final answer. They’ve been around long enough that they have become familiar, almost beyond doubt. Nevertheless, they remain unproven ad hoc hypotheses.

The sentiment that is often asserted is that cosmology works so well that dark matter and dark energy must exist. But a more conservative statement would be that our present understanding of cosmology is correct if and only if these dark entities exist. The onus is on us to detect dark matter particles in the laboratory.

That’s just the first conventionalist stratagem. I could given many examples of violations of the other three, just from my own experience. That would make for a very long post indeed.

Instead, you should go read Merritt’s paper. There are too many things there to discuss, at least in a single post. You’re best going to the source. Be prepared for some cognitive dissonance.


Tension in the Hubble constant

Tension in the Hubble constant

There has been some hand-wringing of late about the tension between the value of the expansion rate of the universe – the famous Hubble constant, H0, measured directly from observed redshifts and distances, and that obtained by multi-parameter fits to the cosmic microwave background. Direct determinations consistently give values in the low to mid-70s, like Riess et al. (2016): H0 = 73.24 ± 1.74 km/s/Mpc while the latest CMB fit from Planck gives H0 = 67.8 ± 0.9 km/s/Mpc. These are formally discrepant at a modest level: enough to be annoying, but not enough to be conclusive.

The widespread presumption is that there is a subtle systematic error somewhere. Who is to blame depends on what you work on. People who work on the CMB and appreciate its phenomenal sensitivity to cosmic geometry generally presume the problem is with galaxy measurements. To people who work on local galaxies, the CMB value is a non-starter.

This subject has a long and sordid history which entire books have been written about. Many systematic errors have plagued the cosmic distance ladder. Hubble’s earliest (c. 1930) estimate of H0 = 500 km/s/Mpc was an order of magnitude off, and made the universe impossibly young by what was known to geologists at the time. Recalibration of the distance scale brought the number steadily down. There followed a long (1960s – 1990s) stand-off between H0 = 50 as advocated by Sandage and 100 as advocated by de Vaucouleurs. Obviously, there were some pernicious systematic errors lurking about. Given this history, it is easy to imagine that even today there persists some subtle systematic error in local galaxy distance measurements.

In the mid-90s, I realized that the Tully-Fisher method was effectively a first approximation – there should be more information in the full shape of the rotation curve. Playing around with this, I arrived at H0 = 72 ± 2. My work relied heavily on the work of Begeman, Broeils, & Sanders and in turn on the distances they had assumed. This was a much large systematic uncertainty. To firm up my estimate would require improved calibration of those distances quite beyond the scope of what I was willing to take on at that time, so I never published it.

In 2001, the HST Key Project on the Distance Scale – the primary motivation to build the Hubble Space Telescope – reported H0 = 72 ± 8. That uncertainty was still plagued by the same systematics that had befuddled me. Since that time, the errors have been beaten down. There have been many other estimates of increasing precision, mostly in the range 72 – 75. The serious-minded cosmologist always worries about some subtle remaining systematic error, but the issue seemed finally to be settled.

One weird consequence of this was that all my extensive notes on the distance scale no longer seemed essential to teaching graduate cosmology: all the arcane details that had occupied the field for decades suddenly seemed like boring minutia. That was OK – about that time, there finally started to be interesting data on the the cosmic microwave background. Explaining that neatly displaced the class time spent on the distance scale. No longer were the physics students stopping to ask, appalled, “what’s a distance modulus?”; now it was the astronomy students who were appalled to be confronted by the spherical harmonics they’d seen but not learned in quantum mechanics.

The first results from WMAP were entirely consistent with the results of the HST key project. This reinforced the feeling that the problem was solved. In the new century, we finally knew the value of the Hubble constant!

Over the past decade, the best-fit value of H0 from the CMB has done a slow walk away from the direct measurements in the local universe. It has gotten far enough to result in the present tension. The problem is that the CMB doesn’t measure the Hubble constant directly; it constrains a multi-dimensional parameters space that approximately projects to a constant of the product ΩmH03, as illustrated below.

Best fit values of the Hubble constant and the mass density from CMB satellite experiments (labeled). The blue lines demarcate the trench allowed in the space by the Planck data. Only the narrow space between the lines is allowed; the region above and below is excluded. The best fit values have simply marched along the floor of this trench over time.

Much of the progress in cosmology has been the steady reduction in the allowed range in the above parameter space. The CMB data now allow only a narrow trench. I worry that it may wink out entirely. Were that to happen, it would falsify our current model of cosmology.

For now the only thing that seems to be happening is that the χ2 for the CMB data  is ever so slightly better for lower values of the Hubble constant. While the lines of the trench represent no-go zones – the data require cosmological parameters to fall between the lines – there isn’t much difference along the trench. It is like walking along the floor of the Grand Canyon: exiting by climbing up the cliffs is disfavored; meandering downstream is energetically favored.

That’s what it looks like to me. The CMB χ2 has meandered a bit down the trench. It is not obvious to me that the current Planck best-fit is all that preferable to that from WMAP3. I have asked a few experts what would be so terrible about imposing the local distance scale as a strong prior. Have yet to hear a good answer, so chime in if you know one. If we put the clamps on H0 it must come out somewhere else. Where? How terrible would it be?

This is not an idle question. If one can recover the local Hubble constant with only a small tweak to, say, the baryon density, then fine – we’ve already got a huge problem there with lithium that we’re largely ignoring – why argue about the Hubble constant if this tension can be resolved where there’s already a bigger problem? If instead, it requires something more radical, like a clear difference from the standard number of neutrinos, then OK, that’s interesting and potentially a big deal.

So what is it? What does it take to reconcile to Planck with local H0? Since this is an issue of geometry, I suspect it might be something like the best fit geometry of the universe becoming ever so slightly not-flat, at the 2σ level instead of 1σ.


While I have not come across a satisfactory explanation of what it would take to reconcile Planck with the local distance scale, I have seen many joint analyses of Planck plus lots of other data. They all seem consistent, so long as you ignore the high-L (L > 600) Planck data. It is only the high-L data that are driving the discrepancy (low L appear to be OK).

So I will say the obvious, for those who are too timid: it looks like the systematic error is most likely with the high-L data of Planck itself.