Measuring the baryon excess

There are two independent ways to measure the baryon content of the universe. Both ways measure the ratio $\eta$ of the present-day number density of baryons, $n_{_B}$, to the present-day number density of photons, $n_\gamma$. The results from the two experiments agree to remarkable accuracy. The agreement is not only between two experimental methods but also between two epochs in the development of the universe: neutrino decoupling and recombination.

Baryon number from BBN

In the big-bang model of the universe, production of light elements (``big-bang nucleosynthesis'') occurs when the universe has cooled to the binding energy of the light nuclei, $T \sim 1 {\rm MeV}$. The formation rates of the light elements are sensitive to the nucleon density, which to good approximation equals the baryon density. Fig. 1 shows how the primordial abundances of several light elements vary with $\eta_{10} = \eta\ensuremath{\cdot 10^}{10}$ [1]. The small boxes indicate the 1-$\sigma$ primordial concentrations extracted from experiment; the larger boxes indicate the ``concordance'' values. The blue-shaded background indicates the ``concordant'' region:

$$2.6 < \eta_{10} < 6.2.$$

As far as I can tell, ``concordance'' means that the values of $\eta$ derived from the various observables agree roughly, but that the uncertainties from experiment and theory are large enough that it does not make sense to quantify the agreement.

Figure 1: Dependence of the primordial light element abundances on $\eta _{10} (= \eta \ensuremath {\cdot 10^}{10})$

Baryon number from the CMB

The WMAP CMB anisotropy measurements provide the second experimental measurement of $n_{_B}$. The position of the peaks and troughs as well as the relative amplitudes are sensitive to many cosmological parameters, including $\Omega_{_B} h^2$. A fit to the WMAP sky maps extracts the age of the universe, decoupling time, $\Omega_m h^2$, $\Omega_{_B} h^2$ and $\Omega h^2$ simultaneously [2]. (For an interesting discussion of how $\Omega_{_B} h^2$ in particular affects the power spectrum, see [3].) The combined WMAP and BBN result yields

$$\eta = \left(6.1^{+0.3}_{-0.2}\right)\cdot 10^{-10}.$$

Figure 2: WMAP acoustic peaks in the temperature angular power spectrum (TT) and temperature-polarization cross-power spectrum (TE). The value of $n_{_B}$ is determined mostly by the ratio of the amplitudes of the first and second TT peaks.

Implications

The experimental value of $n_{_B}$ raises two disturbing questions. ``Why is the value so small?'' and ``Why is the value so big?'' A variable that could, as far as we know, choose any value from zero to fifty times the measured value (when $\Omega_b h^2$ would be ${\cal O}(1)$) but chooses to be as small as it is must have a compelling reason to do so. The smallness of $\eta$ suggests that the ``natural'' value for $\eta$ is zero, but that through some mechanism it is made to deviate slightly from this natural value. $\eta = 0$ is indeed the most reasonable value to expect; it is the value that would arise if the universe were matter-antimatter-symmetric -- every baryon would have an antibaryon partner, and the net number of baryons would be zero. The great puzzle is why this number is nonzero, as we will discuss in greater detail in Sec. 4.