Fr.: rapport baryon-photon
The → baryon number compared with the number of photons in the → Universe. The baryon-photon ratio can be estimated in a simple way. The → energy density associated with → blackbody radiation of → temperature T is aT4, and the mean energy per photon is ~kT. Therefore, the number density of blackbody photons for T = 2.7 K is: nγ = aT4/kT = 3.7 x 102 photons cm-3, where a = 7.6 x 10-15 erg cm-3 K-4 (→ radiation density constant) and k = 1.38 x 10-16 erg K-1 (→ Boltzmann's constant). The number density of baryons can be expressed by ρm/mp, where ρm is the mass density of the Universe and mp is the mass of the → proton (1.66 x 10-24 g). → CMB measurements show that the baryonic mean density is ρm = 4.2 x 10-31 g cm-3 (roughly 5% of the → critical density). This leads to the value of ~ 2 x 10-7 for the number density of baryons. Thus, the baryon/photon ratio is approximately equal to η = nb/nγ = 2 x 10-7/3.7 x 102 ~ 5 x 10-10. In other words, for each baryon in the Universe there is 1010 photons. This estimate is in agreement with the precise value of the baryon-photon ratio 6.14 x 10-10 derived with the → WMAP. Since the photon number and the baryon number are conserved, the baryon-photon ratio stays constant as the Universe expands.