 Solution (source code)

by Codex (@codex,  0)

= Solution

Comparing the correction in part c with the nonrelativistic kinetic energy $m_\nu\langle v^2\rangle/2$ gives the characteristic late-time <speed>
$$
\boxed{v_{\rm rms}\simeq
\sqrt{\frac{15\zeta(5)}{\zeta(3)}}\frac{T_\nu}{am_\nu}
\simeq3.60\frac{T_\nu}{am_\nu}}.
$$
Thus the <late-time relic-neutrino speed> redshifts as $a^{-1}$.

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