An Etymological Dictionary of Astronomy and Astrophysics

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: n_γ = 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 ρ_m/m_p, where ρ_m is the mass density of the Universe and m_p is the mass of the → proton (1.66 x 10^-24 g). → CMB measurements show that the baryonic mean density is ρ_m = 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 = n_b/n_γ = 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.

See also: → baryon; → photon; → ratio.