The Universe today is believed to be dominated by dark energy. In fact, it is believed that the dark energy may take the form of a cosmological constant, in which case its energy density has been a constant throughout the history of the Universe. Radiation and matter are also present today and have been present for most of the history of the Universe. However, as the Universe expands, matter and radiation are diluted; their densities decrease at later times. If you know about the scale-factor of the Universe, $a$, we can say that $\rho_{\gamma}\propto a^{-4}$, $\rho_{m}\propto a^{-3}$, and $\rho_{\Lambda} = constant$, where $\rho_{\gamma}$ is the density of radiation, $\rho_{m}$ is the density of matter, $\rho_{\Lambda}$ is the density of the cosmological constant. Tracing back from out dark-energy dominated Universe, we get to a matter dominated Universe, and then further back still, we get radiation domination.
However, it is also believed that the very early Universe went through a period of accelerated expansion called inflation. Here, the Universe expands as if it were dark-energy dominated; its volume increases rapidly and it is supercooled. This process doesn't last long. Also, when inflation comes to an end, the energy is used to "reheat" the Universe.