# What is the current measured (i.e. model independent) density of hydrogen $H$ in the universe?

The question came up in this thread: What is the current value for the temperature at which Recombination took place? I was under the impression that we had an independent measurement of Hydrogen in the current universe in order to test out the predictions of BBN. One of the respondents seems to be suggesting that there is no such measurement and that we need to have a model of Cosmology before we can estimate the average density of H and He.

So is there a current measurement of the $$H$$ (neutral and ionized) density that doesn't rely on the assumptions of $$\Lambda$$CDM? If not, how do we know that the prediction of BBN of ~75% is correct?

• One could argue that there are no model-independent measurements of anything. – AccidentalFourierTransform Nov 27 '18 at 20:59
• @AccidentalFourierTransform - Yes, if you wanted to be pedantic, you certainly could argue that. – Quarkly Nov 27 '18 at 21:07
• There is no accurate measurement. The current baryonic density of the universe is estimated from the CMB and corroborated with estimates of the primordial abundances of He and D. – Rob Jeffries Nov 27 '18 at 22:05
• AFT's comment is completely correct, and is especially true in cosmology. By its very nature, cosmology - like all of astronomy, but even more so than the other subfields - studies things that we can't directly measure in the lab, so virtually everything we have to say about cosmology assumes some model. That certainly includes the density of hydrogen through the universe - how would we possibly measure that without assuming some model? – tparker Nov 28 '18 at 3:27
• @tparker - it is clear from my description of the problem that I was looking for a method free from the cold, dark matter and anti-gravity assumptions of $\Lambda CDM$. You are arguing just for the sake of arguing. – Quarkly Nov 28 '18 at 19:22

There are only lower limits to the measured baryon density in the local universe.

The baryon density should be about 4.6% of the critical density of the universe (about 6 H atoms per cubic metre). This value arises from modelling of the cosmic microwave background, but before that it had already been estimated at around that level from determinations of the primordial helium and deuterium abundances.

The amount of luminous baryonic matter in the form of stars is much less than 1% of the critical density; for a long time there has been a second "dark matter problem" - that most of the baryonic matter was undetected.

There has however been much progress in finding hot gas in clusters of galaxies and warm gas in halos around galaxies and in filamentary structures between galaxies. This warm-hot intergalactic medium may account for 40% of the required baryons and it has been claimed recently that it is sufficient to account for all the "missing baryons" (Nicastro et al. 2018).

An excellent review of the topic is provided by Shull et al. (2012) who conclude that the current census (see picture below) gets to within $$29\pm 13$$% of the value suggested by the CMB, but I think it is fair to say that others would regard an uncertainty of this size as highly optimistic.

Pie chart showing the likely contributions to a whole pie that represents the 4.6% of the critical density suggested for baryons by CMB measurements (Shull et al. 2012).

Note that most of these measurements depend linearly (or in some cases, to the power 1.5) on the current Hubble parameter, since this is used to estimate (large) distances and volumes.

As a final comment, I would note that the "model dependence" of the 4.6% number boils down to the factor by which we think the universe has expanded since (a) the epoch of primordial nucleosynthesis and (b) the epoch of recombination, since our measurements of those phenomena yield estimates of the baryon densities at those (very different) epochs, and baryon number is conserved.

• What are the units on the pie chart? – Quarkly Nov 28 '18 at 2:00
• @DonaldAirey Percentage points. – tparker Nov 28 '18 at 3:12
• Yeah, I thought of that. The total is 105.7%. – Quarkly Nov 28 '18 at 12:47
• @DonaldAirey Error bars. Plus you need to read the caption in the paper. The pink and blue measurements are not independent and their sum is better determined to be $25\pm 8$%. Using this for pink+blue adds up to 100%. – Rob Jeffries Nov 28 '18 at 12:53
• OK. I'm still digesting the Shull article, but I've got a big picture item. The values here are quoted in terms of $\Omega_B h^2$. So that means we've accounted for (100% - 29%) = 71% of the Baryons of the theoretical value of 4.6% (WMAP) or 4.8% (Plank) of critical density. So that means we've observationally accounted for 0.71 * 0.048 = 0.034 (3.4%) of the baryons w/r/t critical density. How do I go from this value to a present day value of $\rho H$ without going through BBN? – Quarkly Dec 5 '18 at 1:30