How many CMBR photons have been lost ?

Please ponder a co-moving volume, which winds up expanding to become 1 cubic cm, today, z=0. That co-moving volume today contains ~400 CMBR photons (Maoz. Astrophys. in a Nutshell, eq. 9.25) ([math]n_{\gamma}[/math]), and about a billionth as many baryons ([math]n_e \approx n_B[/math]). Since cosmic re-ionization, back at z ~ 10, our space-time has been filled with a diffuse, and nearly completely ionized, plasma. Thus, if the 'Look-back Time' to the re-ionization epoch is ~12 Gyr ([math]t_{LB_{10}}[/math]), then the number of photon-free-electron Thompson scatterings, occurring in our comoving cubic volume, since that ancient eon, has been (roughly):

where we have employed the photon-to-baryon ratio [math]\eta \equiv n_{\gamma} / n_B[/math]. Plugging in the numerical values, I compute [math]N \approx 1 \times \eta_9[/math] such scatterings, where [math]\eta_9 \equiv \eta \times 10^9[/math]. Thus, in over 10 billion years of crossing cosmological distances, only a few tenths of a percent of the CMBR photons have been lost (to Thompson scattering).

What about Cosmic Rays, could CRs be a considerable component of [math]n_B[/math] ?? Or, might metals have significantly larger Compton Scattering cross-sections ?? According to NRAO, the CMBR is by far the most prominent peak in earth-received, cosmologically originating, extra-terrestrial radiation:

Metals reside, in the 'Lyman-alpha forest' inter-galactic clouds, at low levels, but metals may have scattering cross-sections that are enormous, in comparison to the Thompson profile, of lone electrons.

Edited July 31, 201114 yr by Widdekind