What is the Baryon Density, Anyway?

To continue… we had been discussing the baryon content of the universe, and the missing baryon problem. The problem exists because of a mismatch between the census of baryons locally and the density of baryons estimated from Big Bang Nucleosynthesis (BBN). How well do we know the latter? Either extremely well, or perhaps not so well, depending on which data we query.

At the outset let me say I do not doubt the basic BBN picture. BBN is clearly one of the great successes of early universe cosmology: it is pretty clear this is how the universe works. However, the absolute value we obtain for Ωb depends on the mutual agreement of independent measurements of the abundances of different isotopes. These agree well enough to establish the BBN paradigm, but not so well as to discount all debate about the exact value of Ωb – contrary to the impression one might get from certain segments of the literature.

BBN is thoroughly discussed elsewhere so I won’t belabor it here. In a nutshell, the primordial abundance of the isotopes of the light elements – especially deuterium, helium, and lithium relative to hydrogen – depends on the baryon density. Each isotope provides an independent constraint. This is perhaps the most (only?) over-constrained problem in cosmology.

It is instructive to look at the estimates of the baryon density over time. These are usually quoted as the baryon density multiplied by the square of the Hubble parameter normalized to 100 km/s/Mpc (Ωbh2). This is a hangover from the bad old days when we didn’t know H0 to a factor of 2.


The graph shows the baryon densities estimated by various methods by different people over the years. It starts with the compilation of Walker et al. (1991). By this time, BBN was already a mature subject, with an authoritative answer based on evidence from all the isotopes. Ωbh2 = 0.0125 ± 0.0025. It was Known, Khaleesi.

In the mid-90s there was a debate about the primordial deuterium abundance, largely between Hogan and Tytler. Deuterium (red tirangles) is a great isotope to measure for BBN because it is very sensitive to the baryon density, as it tends to get gobbled up into heavier isotopes like helium when there are lots of baryons around to react with. Moreover, one could measure it in the absorption along the line of sight to high redshift QSOs, presumably catching it before any nasty interstellar processing has polluted the primordial abundance. Unfortunately, Hogan found a high D/H (and hence a low baryon density) while Tytler found low D/H (hence high Ωbh2). This is a rare case when one side (Hogan) actually admitted error, and the standard density shot up to 0.019. At the time (1998) that seemed outrageously high, 2.6σ above the previous standard value. But we had bigger problems to wrap our head around (Λ) at the time, so this was accepted without much fuss.

The other elements (helium and lithium) preferred something in between at that time. Their uncertainties were large enough this didn’t seem a big deal. Helium in particular is notoriously hard to pin down. Not only is the measurement hard to make, but helium (unlike deuterium) is not particularly sensitive to the baryon density. You get about a quarter helium by mass out of BBN for any reasonable baryon density, so it is a great indicator that the basic picture is correct. But you really have to nail down the third decimal point to help distinguish between slightly lower or higher Ωb. So the new normal became Ωbh2 = 0.019 ± 0.001.

That was the summation of decades of work, but it wasn’t to last long. In 2000, cosmic microwave background (CMB) experiments like BOOMERanG and MAXIMA began to resolve the acoustic power spectrum. A funny thing emerged: the second peak was lower than expected. (At least by other people. I totally nailed this prediction.) In order to explain the low second peak conventionally (in the context of ΛCDM), one had to crank up the baryon density. This first point from the CMB (blue in plot above) was well above previously suspected levels.

Note the dotted lines in the figure. These denote the maximum baryon density (horizontal line) before the first relevant CMB data (vertical line). No isotope of any light element had ever suggested Ωbh2 > 0.02 prior to CMB constraints. Once those became available, this changed.

The change happened first to deuterium, which has not suggested Ωbh2 < 0.02 since the CMB said so. Helium was slower to respond, but it has also drifted slowly upward. Lithium has remained put. This is a serious problem that has not been satisfactorily resolved. The general presumption seems to be that this is a detail to be blamed on stellar rotation or some similarly obscure mechanism.

Different communities work on each of these elements. Deuterium is the subject of high redshift astronomy, a field closely coupled to cosmology. Helium is the subject of nearby galaxies, a field aware of cosmology but less strongly tied to it. Lithium is measured in stars, a field that is not coupled to cosmology. Given the long history of confirmation bias in cosmology, it is hard not to be suspicious of the temporal variation in BBN baryon density estimates. The isotope most closely associated with cosmology, deuterium, quickly fell in line with the “right” result from the CMB. Helium has more gradually followed suit, while lithium continues to prefer lower baryon densities.

I do not doubt the sincerity of any particular measurement. But people talk. They have arguments about what is right and why. The communities that are closest are most likely to influence each other. Those further apart are less likely to be swayed. If we were suffering from confirmation bias, this is what it would look like.

The ΛCDM picture requires us to believe the CMB value, currently  Ωbh2 = 0.02230 ± 0.00023 (Planck 2015). You simply cannot fit the acoustic power spectrum with a number much different. Modern deuterium measurements are consistent with that, within the errors, so that has to be right, no? Lets just ignore lithium.

If instead we ignore the CMB and its associated baggage, this is not at all obvious. Perhaps the pre-CMB deuterium measurement is the one to trust. That is a bit higher than lithium, but consistent within the errors. Helium can go either way. So from a pure BBN (no CMB) perspective, maybe it is lithium and the other isotopes that are right and it is CMB fits that are misleading.

Where does this leave us with the missing baryons? The figure below shows the time evolution of the baryon density. The area is proportional to Ωbh2. This has grown over time, by an amount greater than the stated uncertainties (the circles show the change in area allowed). The baryon density has nearly doubled, being now ~4σ above the Known value of Walker.


As the baryon density has grown, the missing baryon problem has grown worse. If we still had the classical Walker baryon density, there would be no missing baryon problem at al.  Indeed, Shull’s inventory is a bit too large, though it is consistent within the errors. If we go up to the pre-CMB deuterium value, then there is a missing baryon problem. It is big enough to solve the cluster problem in MOND, but without a lot left over. If we insist on the CMB-fitted baryon density, then the missing baryon problem is severe, at a level where it is hard to figure where else they could be.

IF ΛCDM is the right picture, then I think a high baryon density is unavoidable. Accepting this, there must then be something wrong with lithium. There is no lack of papers motivated by this line of reasoning, though the most common approach seems to be to ignore lithium entirely. I’ve heard a lot of talks bragging about the excellent agreement between BBN and the CMB, but this  really only applies to post-CMB deuterium.

IF BBN, as originally posed, is correct so that lithium and the other pre-CMB measurements are not misleading, then it becomes impossible to fit the CMB with pure General Relativity. This is the case even if we spot it non-baryonic cold dark matter and dark energy. This situation might be considered a motivation to seek extensions of the theory.

Regardless of where the right answer ultimately lies, there is real tension between primordial lithium measurements and the ΛCDM interpretation of the CMB. Something is fishy in the state of the early universe.