# Why does this distribution function depend on time and not temperature?

When reading Sterile neutrino hot, warm, and cold dark matter I came across the following momentum distribution function for a neutrino species $$\alpha$$:

$$\tag{5.8} f(p,t) = \frac{1}{e^{E(p)/T + \eta_{\nu_\alpha}}+1}$$

where $$\eta_{\nu_\alpha}= \mu_{\nu_\alpha }/T$$ and $$E(p) \approx p$$.

Why is the function $$f$$ a function of variables $$p$$ (momentum) and $$t$$ (time) when the RHS shows that the function only depends on $$p$$ and on $$T$$ (temperature)?

On another article Dodelson-Widrow production of sterile neutrino Dark Matter with non-trivial initial abundance it is stated that $$f(p,t)$$ and $$f(p,T)$$ are equivalent.

But how can this be so? How can temperature and time be equivalent?