This could be understood intuitively: for an extraordinary particle in a square box, doubling the size of a side of the field decreases the density (and hence power density) by a factor of eight (23). Matter is something whose power density scales with the inverse cube of the size issue, i.e., ρ ∝ a−3, whereas radiation is anything which scales to the inverse fourth energy of the scale factor (ρ ∝ a−four).
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