The Big Bang — Question 7

Question 7

Baryon-to-photon ratio turns a radiation count into a matter density

Use present photon density 411 cm$^{-3}$ and $\eta=6.0\times10^{-10}$. Treat the mean baryon mass as $1.67\times10^{-27}$ kg.

1. Calculate baryon number density per cubic meter and mass density.

2. Find the number of photons per baryon and the mean volume per baryon.

Question 7 - Solution

Baryon-to-photon ratio turns a radiation count into a matter density

(a) Method and calculation

$$\boxed{n_b=\eta n_\gamma=(6.0\times10^{-10})(411\times10^6)=.2466\ {\mathrm{m^{-3}}}}.$$$$\boxed{\rho_b=n_bm_b=4.11822\times10^{-28}\ {\mathrm{kg/m^3}}}.$$

(b) Interpretation and further calculation

$$\boxed{n_\gamma/n_b=1/\eta=1.66667\times10^9}.$$$$\boxed{V_{\mathrm{per\ baryon}}=1/n_b=4.05515\ {\mathrm{m^3}}}.$$

Physical check

These are cosmic mean densities; galaxies, stars and voids differ enormously from this average.