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?


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