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Primordial Nucleosynthesis, Cosmic Microwave Background and Neutrinos

We report the results of a recent likelihood analysis combining the primordial nucleosynthesis and the BOOMERanG and MAXIMA-1 data on cosmic microwave background radiation anisotropies. We discuss the possible implications for relic neutrino background of a high value for the baryonic matter content of the universe, larger than what is expected in a standard nucleosynthesis scenario.

In this contribution we report on a combined analysis of the dependence of CMBR anisotropies and BBN on the energy fractions Ω B h 2 and Ω ν h 2 = N ν Ω 0 ν h 2 for massless neutrinos (N ν standing for the effective neutrino number and Ω 0 ν h 2 for the energy contribution of a single ν − ν specie). This is aimed to test the standard and degenerate BBN scenario, using the recent results of the BOOMERanG [1] and MAXIMA-1 [2] CMBR experiments and the measurements of 4 He, D and 7 Li primordial abundances.
The theoretical tools necessary to achieve this goal are nowadays rather robust. A new generation of BBN codes have been developed [3][4][5], which give the 4 He mass fraction Y p with a theoretical error of few per mille, this effort being justified in view of the small statistical error which is now quoted in the Y p measurements. On the other hand, the theoretical predictions on the CMBR anisotropies angular power spectrum have also recently reached a 1% level accuracy. An important new insight is represented by the recent results obtained by the BOOMERanG Collaboration [1]. For the first time, in fact, multifrequency maps of the microwave background anisotropies were realized over a significant part of the sky, with ∼ 10 ′ resolution and high signal to noise ratio. In the last few years many results have been obtained on light element primordial abundances as well [6]. The 4 He mass fraction Y p , has been measured with a 0.1% precision in two independent surveys, from regression to zero metallicity in Blue Compact Galaxies, giving a low value Y (l) p = 0.234±0.003, and a high one Y (h) p = 0.244±0.002, which are compatible at 2σ level only, may be due to large systematic errors. In our analysis [7] we adopted the more conservative value Y p = 0.238±0.005. A similar controversy holds in D measurements, where observations in different Quasars Absorption line Systems (QAS) lead to the incompatible results Y (l) We performed our analysis for both low and high D data. Finally, the most recent estimate for 7 Li primordial abundance, from the Spite plateau observed in the halo of POP II stars, gives Y7 Li = (1.73±0.21) 10 −10 . The light nuclide yields strongly depend on the baryon matter content of the universe, Ω B h 2 . In particular, assuming a standard BBN scenario, i.e. vanishing neutrino chemical potentials, the likelihood analysis gives, at 95% C.L. [4], (1) Regarding CMBR data, the anisotropy power spectrum, C ℓ , was measured in a wide range of angular scales from multipole ℓ ∼ 50 up to ℓ ∼ 600, with error bars of the order of 10%, showing a peak at ℓ peak = (197±6) with an amplitude DT 200 = (69±8)µK. While the presence of such peak, compatible with inflationary scenario, was already suggested by previous measurements [8], the absence of secondary peaks after ℓ ≥ 300 with a flat spectrum with an amplitude of ∼ 40µK up to ℓ ∼ 625 was a new and unexpected result. This result obtained then an impressive confirmation by the MAXIMA-1 [2] experiment up to ℓ ∼ 800.
As already pointed out [9], the values in Eq. (1) for Ω B h 2 , though in the correct order of magnitude, are however somehow smaller than the baryon fraction which more easily fit the CMBR data. In fact, the lack of observation of a secondary peak in the anisotropy power spectrum at small scales may be a signal in favour of a larger Ω B h 2 ∼ 0.03, since increasing the baryon fraction enhances the odd peaks only.
It has been stressed [4] that a simple way to improve the agreement of observed nuclide abundances with Ω B h 2 ≥ 0.02 is to assume non vanishing neutrino chemical potentials at the BBN epoch, a scenario already extensively studied in the past [10]. The effect of neutrino chemical potentials µ α , with α the neutrino specie, is twofold. A non-vanishing ξ α = µ να /T ν , contribute to N ν implying a larger expansion rate of the universe with respect to the non-degenerate scenario, and a higher value for the neutron to proton density ratio at the freeze-out. Furthermore, a positive value for ξ e means a larger number of ν e with respect toν e , thus enhancing n → p processes.
Increasing N ν also weakly affects the CMBR anisotropy spectrum in two ways. The growth of perturbations inside the horizon is in fact lowered, resulting in a decay of the gravitational potential and hence in an increase of the anisotropy near the first peak. Moreover, the size of horizon and sound horizon at the last scattering surface is changed, and this, with additional effects in the To test the degenerate BBN scenario we performed a likelihood analysis of the data. First, to constrain the values of the parameter set (ξ e , N ν , Ω B h 2 ) from the data on 4 He, D and 7 Li we define a total likelihood function, L N ucl (N ν , Ω B h 2 , ξ e ) [4,7]. Since the effect of a positive ξ e can be compensated by larger N ν , we have chosen to constrain this parameter to be N ν < 16, well outside the 95% upper limit on N ν from the BOOMERanG and MAXIMA-1 data (see below). The other two parameters are chosen in the following ranges, −1 ≤ ξ e ≤ 1 and 0.004 ≤ Ω B h 2 ≤ 0.110.
In the figure we summarize the main result of our analysis. In the Ω B h 2 − N ν plane we show the 95% C.L. likelihood regions for both the high and low D measurements, as well as the analogous contours for standard BBN, obtained running our code with ξ e = 0. In the same plot we show the 68 and 95 % C.L. regions obtained by CMBR data.
We observe that the standard BBN, ξ e = 0, and CMBR data analysis lead to quite different val-ues for Ω B h 2 . This can be clearly seen from the reported 95% results, but we have verified that the 99% C.L. contour for high D has no overlap with the region picked up by BOOMERanG and MAXIMA-1 data, and a very marginal one for low D.
For the degenerate scenario, increasing N ν , the allowed intervals for Ω B h 2 shift towards larger values. However the high D values require a baryon content of the universe energy density which is still too low, Ω B h 2 ≤ 0.018, to be in agreement with CMBR results. A large overlap is instead obtained for the low D case, whose preferred Ω B h 2 span the range 0.012 ≤ Ω B h 2 ≤ 0.036. As expected, a larger N ν helps in improving the agreement with the high CMBR Ω B h 2 value, but is important to stress that a large value for N ν is not preferred by the CMBR data alone, being, in this case, the best fit N ν ∼ 3. If we only consider the 95% overlap region we get the following conservative bounds 1 : 4 ≤ N ν ≤ 13 , 0.024 ≤ Ω B h 2 ≤ 0.034. (2) In this region ξ e varies in the range 0.07 ≤ ξ e ≤ 0.43. As we said, values N ν ≥ 3, as suggested from our analysis, can be either due to weak interacting neutrino degeneracy, or rather to other unknown relativistic degrees of freedom.