Total number of particles in the universe (according to Planck Surveyor measures, 2018)

Question

Recently, Marco Ajello et al. (2018) has estimated the total number of photons in the whole observable universe as: $$N_\gamma \approx 4\cdot 10^{84}.$$ On the other hand, the ratio of baryons to photons or the baryon abundance is defined as: $$\eta \equiv \frac{N_b}{N_\gamma} \simeq 2.75 \times 10^{-8} \; \Omega{_b}h^2$$ being $\Omega{_b}h^2 = 0.0224 \pm 0.0001$ according to the Planck surveyor measures of 2018. All these numbers, suggest (if I am not confusing the data) that the total number of baryons in the universe is about:

$$N_b \approx 2.5\cdot 10^{75}.$$

Is this number in agreement with other experimental measures of baryonic abundance (I have not been able to find a suitable reference), already taking into account the missing baryon problem?

Answer 1

The quantities considered in the question are not directly comparable. The Fermi collaboration (2018) measured the number of photons comprising the extragalactic background light, which is ultraviolet/visible/infrared light produced in galaxies. This is a tiny fraction of the total number of photons in the Universe, which is dominated by the cosmic microwave background (CMB). The photon-to-baryon ratio is the ratio between CMB photons and baryons.