Matter: energy density proportional to R-3
Radiation: energy density proportional R-3 (volume effect) times another R-1 (redshift effect), so R-4.
After about 55,000 years, T ~ 9000 K and the energy density of radiation falls below that of matter: we enter the matter era.
Now, photons and particles are still closely coupled, due to all the free electrons running around. Electrons scatter photons through Thomson scattering, so that photons cannot free stream. The Universe is opaque, and matter and radiation behave as a single fluid.
Imagine a little piece of the Universe, which has an excess amount of matter. It will want to start collapsing under its own gravity. But it can't: the photons are coupled to the particles and keep them from collapsing. So structure (galaxies, stars, clusters, etc) cannot form!
When the temperature of the universe drops below
K or so, when the Universe is ~ 200,000 years old, the electrons and
combine to form atoms. No free electrons are running around, so photons
can free stream and matter decouples from radiation. This is a
important time in the Universe's history: called the epoch
of recombination. The Universe becomes transparent, we see it as the microwave background, and
can start to form...