Number Density vs Energy Density of Radiation and Matter

[cp05]

I was going through my notes preparing for finals (this is my last one hooray!), and I saw that the Number Density of radiation and matter changes at the same rate (N=Na^-3) while the energy density is different (E=Ea^-3 for matter, E=Ea^-4 for radiation). I think I get why the energy densities for matter/radn are different (matter exists in 3 dimensions...while radiation exists in 4 because of time...is that remotely correct?), but I don't understand why the number densities are the same.

Thanks for the help!

 

[member 553083]

The reason why the number densities of radiation and matter are the same is because they are both affected by expansion at the same rate. As space expands, the number of particles of matter and radiation in a given volume decreases, resulting in a decrease in the number density of both. The energy densities are different because the energy of matter is stored in mass, which does not change with the expansion of space, while the energy of radiation is stored in photons, which do change with the expansion of space.