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As the universe expands, both matter and radiation in it become diluted.
However, the universe is also cooling down, meaning that the average energy per particle is getting smaller with time.
Therefore the radiation becomes weaker, and dilutes faster than matter.
Thus with the expansion of the universe, radiation becomes less dominant than matter.
The very early universe is said to have been ' radiation dominated ' and as such radiation controlled the deceleration of expansion.
Later, as the average energy per photon becomes roughly 10 eV and lower, matter dictates the rate of deceleration and the universe is said to be ' matter dominated '.
The intermediate case is not treated well analytically.
As the expansion of the universe continues, matter dilutes even further and the cosmological constant becomes dominant, leading to an acceleration in the universe's expansion.

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