The Matter era began between about 300,000 thousand years after the Big Bang, when the temperature of the background radiation had dropped to around 3000 degrees K, cooler than the surface of the sun, but still hot enough to melt and vaporise most substances. The universe had a radius of maybe one and a half million light years compared to 50,000 light years for our the Milky Way although still a fraction of the size of the modern universe.
When the temperature dropped to about 3000 K, it was cool enough for electrons to form into atoms. Matter and radiation were no longer in a state of equilibrium, with photons being constantly absorbed and re – emitted – this passage from being in a state of equilibrium to not being is called de – coupling. With de – coupling, the universe became transparent to radiation and became matter dominated. Electrons and protons recombine into hydrogen atoms, and matter as we know it, consisting of ordinary atoms, is formed.
Decoupling also results in a lowering of the pressure exerted by radiation on matter (since photons carry momentum, they exert a force on matter on absorption/emission). With the radiation pressure gone it became possible for matter to collapse into stars and galaxies under gravitational attraction. Since the end of the radiation era, the Universe has continued to cool and expand. The temperature of the background radiation has cooled from about 3000 K to about 2.7 K and continues to cool.