Chapter 29, Problem 28E

Continuing the thinking in the last three exercises, convert this energy to an equivalent in mass, use Einstein’s equation $E=m{c}^2$ . Hint: Divide the energy per m³ calculated in Exercise 29.27 by the speed of light squared. Check your units; you should have an answer in kg/m³. Now compare this answer with the critical density. Your answer should be several powers of 10 smaller than the critical density. In other words, you have found for yourself that the contribution of the CMB photons to the overall density of the universe is much, much smaller than the contribution made by stars and galaxies.