Baryon:photon ratio

The primordial Li abundance was sought primarily because of its ability to constrain the baryon to photon ratio in the Universe, or equivalently the baryon contribution to the critical density. In this way, Li was able to complement estimates from 4He, the primordial abundance of which varied only slightly with baryon density. Li also made up for the fact that the other primordial isotopes, 2H (i.e. D) and 3He, were at that time difficult to observe and/or interpret. During the late 1990 s, however, measurements of D in damped Lyman alpha systems (high column-density gas believed to be related to galaxy discs) provided more reliable constraints on the baryon density than Li could do (e.g. [19]). Even more recently, the baryon density has been inferred from the angular power spectrum of the cosmic microwave background radiation, for example from the WMAP measurements [26]. We consider the role of Li plateau observations post WMAP. 

The model has only one parameter, the baryon-to-photon ratio, r/. These abundances, which depend only on t], span some nine orders of magnitude. The synthesis of these light elements strongly depends on the physical conditions of the early Universe, at T about 1 MeV, when t is around 1 second. 

The electroweak scenario is now regarded very unlikely to be true [18]. Two main reasons are (1) light Higgs mass needed for the 1st order phase transition is now experimentally excluded, (2) even if the Higgs mass bound is ignored, the estimated baryon to the photon ratio is too small by more than 10 orders. 

Figure 12. The likelihood distributions, normalized to equal areas under the curves, for the baryon-to-photon ratios (r/io) derived from BBN ( 20 minutes), from the CMB ( few hundred thousand years), and for the present universe (to 10 Gyr z 1).

One of the major achievements in cosmology is that it can account simultaneously for the primordial abundances of H, D, 3He, 4IIc and 7Li but only for a low density universe. The comparison between the observed primordial abundances and the Big Bang nucleosynthesis calculations can allow to impose constraints upon the baryon to photon ratio (rj) in the universe. In particular, for a baryon to photon ratio r/ 3 10 10 the baryonic density parameter of the universe is (Peacock, 1999) ... 

Figure 4. The predictions of standard BBN [22], with thermonuclear rates based on the NACRE compilation [24]. (a) Primordial abundances as a function of the baryon-to-photon ratio tj. Abundances are quantified as ratios to hydrogen, except for He which is given in baryonic mass fraction Yp = Ph/Pb-The lines give the mean values, and the surrounding bands give the la uncertainties, (b) The la abundance uncertainties, expressed as a fraction of the mean value p for each q.

Primordial abundances as a function of baryon density PbOt fraction of critical density il b (these two quantities are directly related to the baryon-to-photon ratio ri see text). The widths of the curves give the nuclear physics uncertainties. The boxes specify the ranges of abundances and densities constrained by observation (there is only an upper limit for He from observation) as given in Buries et al. (1999, 2001). The shaded area marks the density range consistent with all observations (Buries et al. 1999,2001). Symbol D represents deuterium, (Reprinted from Tytler... 

After e annihilation during the early evolution of the Universe, the ratio of baryons to photons is, to a very good approximation, preserved down to the present. The baryon density parameter is defined to be this ratio (at present) r] = n /n r/io =... 

Fig. A1.3. Comparison between observed abundances and abundances predicted by the theory of primordial nucleosynthesis. The horizontal axis shows the ratio r between the number of baryons and the number of photons. The vertical axis shows the mass fraction of helium and the numerical ratios D/H, He/H and li/H. Observational data are represented by boxes with height equal to the error bar. In the case of helium and lithium, there are two boxes, indicating the divergence between different observers. Deuterium holds the key to the mystery, but it is difficult to measure. The region of agreement is shown as a shaded vertical ribbon (after Buries Tytler 1997). A higher level of deuterium would lead to a lower baryonic density, of the order of 2%. This would agree better with the lithium data, which have been remarkably finely established. This idea is supported by E. Vangioni-Flam and shared by myself. (From Tytler 1997.)...

As said above, the sBBN model depends on only one parameter r/, the ratio of the number of baryons rib to the number of photons n7 ... 

The ratios of the anisotropy powers below the peak at l 50, at the big peak at ss 220, in the trough at / 412, and at the second peak at / 546 were precisely determined using the WMAP data which has a single consistent calibration for all Us. Previously, these I ranges had been measured by different experiments having different calibrations so the ratios were poorly determined. Knowing these ratios determined the photon baryon CDM density ratios, and since the photon density was precisely determined by FIRAS on COBE, accurate values for the baryon density and the dark matter density were obtained. These values are Ct h2 = 0.0224 4%, and Vtmh2 = 0.135 7%. The ratio of CDM to baryon densities from the WMAP data is 5.0 1. 

It is then both natural and even compelling to be able to explain the baryon asymmetry quantified by the baryon to the photon number density in the present universe. This ratio is the direct measure of the asymmetry prior to the cosmic disappearance of antimatter. This number is usually given in the form of the baryon to the entropy ratio ub/ns and is of order ft)-10, which seems too small at first one excess of baryon over 1010 B — B pairs led to the present B-dominated universe. But actually this number is often too large to be explained in theoretical models. With this large number the standard electroweak theory fails as the microscopic theory for the baryogenesis, as explained below. 

Helium, the second most abundant element, has significance for cosmology and stellar structure. Most 4He was produced in the Big Bang, and the primordial mass fraction Yp is a constraint on the photon/baryon ratio and thus on the cosmological model. The He mass fraction also affects stellar structure, but He is difficult to measure in stars and so must be inferred from other measurements. On the other hand, He I recombination lines are relatively easy to measure in H II regions, and so a large amount of data is available on He/H in ionized nebulae. 

Apart from the input nuclear cross sections, the theory contains only a single parameter, namely the ratio of the number densities of baryons to photons, r. Because both densities scale as their ratio is constant, barring any non-adiabatic processes. The theory then allows one to make predictions (with well-defined uncertainties) of the abundances of the light elements, D, He, He, and Li. 

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