# Cosmological density fluctuation dependence on scale factor

I want to show that in the radiation-dominated era, $$\delta_H^2 \propto a^{1-n}$$. I know that the wavenumber corresponding to the Hubble scale goes like $$a^{-1}$$ and that $$\delta_H^2 \propto k^3 P(k)$$ and $$P(k) \propto k^n$$, but I am unsure of how to put these together to get the desired result.

• Isn't better suited for Physics SE? – Alchimista Nov 12 '20 at 10:15