Dark Matter — Question 7

Question 7

Cosmological density fractions distinguish dark matter from dark energy

For an illustrative spatially flat model use $\Omega_m=.30$, $\Omega_b=.05$ and negligible radiation today. Let H0=$2.27\times10^{-18}$ s$^{-1}$, G=$6.67\times10^{-11}$ SI and $\rho_c=3H_0^2/(8\pi G)$.

1. Find dark-matter and dark-energy density parameters.

2. Calculate critical density and dark-matter mass density.

Question 7 - Solution

Cosmological density fractions distinguish dark matter from dark energy

(a) Method and calculation

$$\boxed{\Omega_{\mathrm{dm}}=\Omega_m-\Omega_b=.25}.$$$$\boxed{\Omega_\Lambda=1-\Omega_m=.70}.$$

(b) Interpretation and further calculation

$$\boxed{\rho_c\simeq9.22\times10^{-27}\ {\mathrm{kg/m^3}}}.$$$$\boxed{\rho_{\mathrm{dm}}=.25\rho_c\simeq2.31\times10^{-27}\ {\mathrm{kg/m^3}}}.$$

Physical check

Matter includes baryons and dark matter. Dark energy is a separate component with different pressure and expansion behavior; the supplied fractions are model inputs.