I am using Freedman and Kaufmann Textbook for Phy Sci 120 course. I noticed there are some apparently incorrect plots in Chapter 28.
We can use the following 2 equations to calculate the lookback time to a given redshift in a given cosmology:
We know that rho_m = 3x10^-27 kg/m^3 at the present epoch and that rho_r=5x10^-31 kg/m^-3. Given that rho_m scales as (1+z)^3 and rho_r as (1+z)^4 I make the following plot to be compared to the one from book on the right. Clearly these plots are not the same.
The temperature of the CMB today is 2.7K and scales as (1+z) so I make the following plot to be compared to the one from book on the right. The plot from the book is extremely misleading - there is no break at combination - the radiation field does not care that the matter de-couples. At combination the radiation field contains more energy than the KINETIC (free) energy of the matter by factor 10^9. Up until combination it is expending a negligible fraction of its energy to "support" the temperature of the matter, but since this fraction is so small it does not care when the matter decouples. The temperature of the matter would exhibit such a "knee" at combination, but the temperature of the radiation does not.
