## Keith Olive: Big bang nucleosynthesis – concordance of theory and observations May 26, 2008

Posted by dorigo in cosmology, physics, science.
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In the file with my notes on the talks I heard in Albuquerque I have a few more summaries that can be of general interest. So let me offer to you today the following one.

Keith gave a very clear and instructive seminar (slides here) on the status of our understanding of big-bang nucleosynthesis (BBN), the theory which uses well-understood nuclear physics to predict how light elements were forged during a very short time interval after the big bang, when the universe was still dense enough that nuclear reactions were frequent, but not any more so hot that photons would destroy nuclear bounds between protons and neutrons. The calculations of BBN are a formidable evidence for the big bang theory, since the abundance of light elements that are present in the universe but cannot have been formed inside stars -and are thus called “primordial”- is explained to good accuracy.

BBN was the primary vehicle to obtain an estimate of the baryon abundance in the universe in the past, but now WMAP data on the cosmic microwave background -the radiation seeping through the universe in all directions, which originated when the universe became transparent to radiation- does that much more precisely. It is thus more important now to try and match up the abundances of individual elements. BBN has become a test, a definite prediction of what are light element abundances. The prediction can be compared with observations to see whether any effect is not yet well understood.

Deuterium is now the best of the three important light isotopes to study (Helium-4 and Lithium-7 are the others). The uncertainty from BBN in Li-7 is larger, and the discrepancy with observations is also larger: there is currently an interesting problem to solve with this element.

WMAP observations now allow us to compute $\Omega_B = 0.0227 \pm 0.0006$, so the baryon to photon ratio is found to be $\eta_{10} = 6.22 \pm 0.16 \times 10^{-10}$. BBN is thus now a parameterless theory to be used to make comparisons.

Keith pointed out that everything about the energy content of the universe is well determined. The equilibrium at high temperature is maintained by weak interactions. What is important for BBN is the neutron to proton conversion rate; this freezes out at temperature of 1 MeV, so one uses the ratio at that time to determine abundances.

Nucleosynthesis is delayed because of the so-called Deuterium bottleneck: there is a delay in the onset of the forging of light elements because of production and destruction rates. As the temperature drops, energetic photons can still be found in the tail of the energy distribution which are able to break the deuterium bound until we arrive at temperatures of a tenth of a MeV, and then, once deuterium forms and is not immediately broken again, nucleosynthesis proceeds very rapidly. The helium abundance is about 25%, and BBN provides a very good estimate for it. D, He-3, Li-7 are at the level of a tenth of a billionth instead.

To understand nucleosynthesis well there are ten nuclear reactions which are important. Most of these have small uncertainties. Keith showed a plot of the helium mass fraction as a function of $eta_{10}$, which indicates that there is a bit of scattering in the data, but overall results are consistent. Uncertainties are small: of the order of 5% to 10% for the ratio of D/H and He-3/H abundance, while it is still of about 20% for Li-7/H.

Light elements are observed in different places in the universe. He-4 in extragalactic H-II regions, and small irregular galaxies, while Li-7 is observed in the atmosphere of dwarf halo stars: this is a small, $10^{-10}$ abundance. Deuterium abundance data is instead coming from quasar absorption systems, but also local measurements in meteorites. He-3 is also found in meteorites, but there is no site to get a primordial abundance of this element, and you need a model for its evolution.

D/H is all primordial, so every deuterium nucleus comes from the big bang. It is observed in Jupiter, in the interstellar medium, and in meteorites. The best observations comes from quasar absorption systems. There is only a handful of good ones though.

Keith then showed a graph of the D/H versus Si/H abundance ratios. The Si/H quantity is also called “metallicity”, and the graph is usually shown with logarithmic axes whose units are multiples of solar abundances. The two are supposed to be independent. On some scale there should be a trend. Dust clouds in the line of sight of quasars might cause a bias: deuterium absorbs light and one gets a nuclear shift due to the mass relative to hydrogen. The BBN prediction is $10^5 D/H = 2.74^{+0.26}_{-0.16}$ while it is observed that on average $10^5 D/H = 2.82 \pm 0.21$. This is in greast agreement with WMAP results.

He-4 is also primordial. It is measured in low-metallicity extragalactic H-II regions, together with O/H and N/H, the relative oxygen and nitrogen abundances. One plots He-4 abundance as a function of the O/H ratio, and then does a regression towards zero O/H: Oxygen is not primordial, so you have to extrapolate the He-4 abundance to zero to obtain its primordial value. One thus gets the value $0.2421 \pm 0.0021$. This ratio has a tiny error. It looks great: better than it should! Indeed, understanding the systematics is not easy. What was done to extract the He-4 abundance was to assume intensity and equal width for hydrogen and helium, then determine hydrogen reddening and its underlying absorption. One needs to make corrections for those effects.
There are six helium lines that can be used to get the abundance, but one also needs to know the electron density, the temperature, and the underlying helium absorption. In the end one reduces the data and arrives to the value 0.2495 with a total 0.0092 error. The He-4 prediction from WMAP is instead $0.2494 \pm 0.0005$.

Lithium, instead, is problematic. It is observed in dwarf stars with low metallicity. Iron abundance relative to the solar one, Fe/H, can be put on the x axis, and Lithium abundance on the y axis. Old Li/H determinations used to sit at 1.2E-10, but a lot of measurements were carried out over the years, and they typically were all of the order of one to two, in 10^-10 units. As metallicity increases, time increases, so one plots Li/H vs Fe/H to see the evolution in the former, and at low metallicity one measures it.

Among the possible sources for the discrepancy observed, one is stellar depletion. One sees a lack of dispersion in the data: dispersion is consistent with the observational error, quite small. It is very unlikely that all stars destroy lithium consistently within a factor of 3. You can model different stars, but there are a hundred of measurements. One can also play with nuclear rates, but it is hard to do. The BBN predicted value is 4E-10, while observations point to a smaller value, from one to two units of E-10.

One must note at this point that particles in the universe with lifetimes of the order of seconds can change the lithium-7 abundance (decrease it, thus bringing it closer to the observed value), if they have lifetimes of 1000 seconds, while they increase the Li-6 abundance. If a next-to-lightest supersymmetric particle decayed into a gravitino, the stau would form a bound state with helium-4, and change many things. From these studies one obtains “preferred” values of the SUSY parameter space, usually plotted in the gaugino versus scalar mass plot. High gaugino masses, around 2-3 TeV, are favored in this scenario. Gluino masses are of about 9 TeV for a 3 TeV gaugino mass. Scalar masses are not so heavy, but it would be admittedly very hard for the LHC to see a signal of these particles if nature had chosen this point of parameter space.

Going into more exotic alternatives, one may mention that also a varying electromagnetic fine structure constant $\alpha$ would upset the balance for the determination of the freeze-out and He-4 abundance. One can try varying all Yukawa couplings, including a dependence of $\Lambda_{QCD}$ on $\alpha$, consider effects on neutron to proton mass ratio and lifetime, and the deuterium binding energy. Those variations can be tracked with variations of the fine structure constant.

Since helium has a large uncertainty, you can see how it varies with $\Delta h/h$. For positive variations it gets you down to make Li-7 in agreement with observations: $-1.8 \times 10^{-5} < dh/h <2.1 \times 10^{-5}$. It needs to be pointed out that this value is not in agreement with the measured variation of the fine structure constant from quasars. These are different times of course, so you could still hypothesize a oscillating variation with time of $\alpha$. You can make models with a varying $\alpha$ that has a positive variation at BBN times and negative at quasar times.

In conclusion, deuterium and helium abundances are in very good agreement with observed values. There are issues to be resolved there too, however. In Li-7, there are two problems: Li-7 BBN is high compared to observations, and Li-6 is low (but it has a large uncertainty).

1. Paulie - May 26, 2008

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2. Thomas D - May 27, 2008

Not only ‘alpha’, but a lot of other things, may be varied at the same time, since BBN depends on every fundamental force (EM, weak, strong, gravity). Some combinations of such variations may be more compatible with a cosmological variation at smaller redshifts. Watch out…

What is the history of ‘PPC’? It sounds like a slightly larger copy of PASCOS with a bit of SUSY and COSMO mixed in. I thought there were enough conferences already… now if we get a new summer / late spring conference shouldn’t we get rid of one of the old ones?

To be precise, there were FOUR conferences going at the same time in the week 19-23 May: Blois (astroparticle), Planck (Barcelona), PPC (New Mexico) and Frontiers (string cosmo, Paris). That doesn’t seem like good planning!

3. dorigo - May 27, 2008

Hi Thomas,

thank you for your point on the variation of constants. Indeed, we attach too much meaning to the word: we know they are not constant anyway!

About the conferences, they are indeed too many around, in my opinion. Conferences were more useful once – before the web 2.0 era – than they are today, and although they still usually provide a stimulating ground for discussions and exchanges, they cost a lot of money to the budget of universities and research institutes. And since expenses of this kind scale with the number of hired personnel, this compresses the budget to experiments. Take INFN, the italian institute for nuclear physics which pays my salary: the bigger part of its yearly budget goes to salaries… Once that fraction reaches 70% or so, it is going to collapse – we saw it with CNR already.

Cheers,
T.

4. Mandeep Gill - June 5, 2008

Thomas- I’ll note that 3 of the confs you mention are in Europe — a little more expensive for Americans to attend!

Anyway — Tommaso – could you explain how late-decaying particles suppress the Li7 abundance, and not affect the others at all..?

thx much.

5. dorigo - June 6, 2008

Hmmm Mandeep, I believe it is due to the fact that lighter elements get synthetized earlier, so that they do not get affected by the decays. If the time scale of cooking up helium is much shorter than the decay time of a hypothetical particle, its forging will not be affected by a lot of energy released in the decays, but bonds such as that mentioned in the post (with a SUSY stau) may affect the subsequent course of events. Or so I seem to have understood….

Cheers,
T.

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