At the dawn of the 21st century, we were pretty sure we had solved cosmology. The Lambda Cold Dark Matter (LCDM) model made strong predictions for the power spectrum of the Cosmic Microwave Background (CMB). One was that the flat Robertson-Walker geometry that we were assuming for LCDM predicted the location of the first peak should be at ℓ = 220. As I discuss in the history of the rehabilitation of Lambda, this was a genuinely novel prediction that was clearly confirmed first by BOOMERanG and subsequently by many other experiments, especially WMAP. As such, it was widely (and rightly) celebrated among cosmologists. The WMAP team has been awarded major prizes, including the Gruber cosmology prize and the Breakthrough prize.
As I discussed in the previous post, the location of the first peak was not relevant to the problem I had become interested in: distinguishing whether dark matter existed or not. Instead, it was the amplitude of the second peak of the acoustic power spectrum relative to the first that promised a clear distinction between LCDM and the no-CDM ansatz inspired by MOND. This was also first tested by BOOMERanG:
In a nutshell, LCDM predicted a big second peak while no-CDM predicted a small second peak. Quantitatively, the amplitude ratio A1:2 was predicted to be in the range 1.54 – 1.83 for LCDM, and 2.22 – 2.57 for no-CDM. Note that A1:2 is smaller for LCDM because the second peak is relatively big compared to the first.
BOOMERanG confirmed the major predictions of both competing theories. The location of the first peak was exactly where it was expected to be for a flat Roberston-Walker geometry. The amplitude of the second peak was that expected in no-CDM. One can have the best of both worlds by building a model with high Lambda and no CDM, but I don’t take that too seriously: Lambda is just a place holder for our ignorance – in either theory.
I had made this prediction in the hopes that cosmologists would experience the same crisis of faith that I had when MOND appeared in my data. Now it was the data that they valued that was misbehaving – in precisely the way I had predicted with a model that was motivated by MOND (albeit not MOND itself). Surely they would see reason?
There is a story that Diogenes once wandered the streets of Athens with a lamp in broad daylight in search of an honest man. I can relate. Exactly one member of the CMB community wrote to me to say “Gee, I was wrong to dismiss you.” [I paraphrase only a little.] When I had the opportunity to point out to them that I had made this prediction, the most common reaction was “no you didn’t.” Exactly one of the people with whom I had this conversation actually bothered to look up the published paper, and that person also wrote to say “Gee, I guess you did.” Everyone else simply ignored it.
The sociology gets worse from here. There developed a counter-narrative that the BOOMERang data were wrong, therefore my prediction fitting it was wrong. No one asked me about it; I learned of it in a chance conversation a couple of year later in which it was asserted as common knowledge that “the data changed on you.” Let’s examine this statement.
The BOOMERanG data were early, so you expect data to improve. At the time, I noted that the second peak “is only marginally suggested by the data so far”, so I said that “as data accumulate, the second peak should become clear.” It did.
The predicted range quoted above is rather generous. It encompassed the full variation allowed by Big Bang Nucleosynthesis (BBN) at the time (1998/1999). I intentionally considered the broadest range of parameters that were plausible to be fair to both theories. However, developments in BBN were by then disfavoring low-end baryon densities, so the real expectation for the predicted range was narrower. Excluding implausibly low baryon densities, the predicted ranges were 1.6 – 1.83 for LCDM and 2.36 – 2.4 for no-CDM. Note that the prediction of no-CDM is considerably more precise than that of LCDM. This happens because all the plausible models run together in the absence of the forcing term provided by CDM. For hypothesis testing, this is great: the ratio has to be this one value, and only this value.
The prediction for the amplitude ratio A1:2 that I made over twenty years ago remains correct in the most recent CMB data. The same model did not successfully predict the third peak, but I didn’t necessarily expect it to: the no-CDM ansatz (which is just General Relativity without cold dark matter) had to fail at some point. But that gets ahead of the story: no-CDM made a very precise prediction for the second peak. LCDM did not.
LCDM only survives because people were willing to disregard existing bounds – in this case, on the baryon density. It was easier to abandon the most accurately measured and the only over-constrained pillar of Big Bang cosmology than acknowledge a successful prediction that respected all those things. For a few years, the attitude was “BBN was close, but not quite right.” In time, what appears to be confirmation bias kicked in, and the measured abundances of the light elements migrated towards the “right” value – as specified by CMB fits.
LCDM does give an excellent fit to the power spectrum of the CMB. However, only the location of the first peak was predicted correctly in advance. Everything subsequent to that (at higher ℓ) is the result of a multi-parameter fit with sufficient flexibility to accommodate any physically plausible power spectrum. However, there is no guarantee that the parameters of the fit will agree with independent data. For a long while they did, but now we see the emergence of tensions in not only the baryon density, but also the amplitude of the power spectrum, and most famously, the value of the Hubble constant. Perhaps this is the level of accuracy that is necessary to begin to perceive genuine anomalies. Beyond the need to invoke invisible entities in the first place.
I could say a lot more, and perhaps will in future. For now, I’d just like to emphasize that I made a very precise, completely novel prediction for the amplitude of the second peak. That prediction came true. No one else did that. Heck of a coincidence, if there’s nothing to it.