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Before electron-positron annihilation, photons, electrons, and positrons share one temperature. Their effective entropy degrees of freedom areThe neutrinos have already undergone thermal decoupling in cosmology, so $T_{\nu }a$ remains constant and they receive none of the electron-positron entropy. In the still-coupled electromagnetic plasma, cosmological entropy conservation givesThe decoupled neutrino temperature at the same later time is $T_{\nu }=T_{\mathrm{before}}{a}_{\mathrm{before}}/a$. Dividing the two relations gives the Cosmic neutrino background temperatureThis instantaneous-decoupling calculation neglects the small reheating correction from non-instantaneous neutrino decoupling.

The entropy density isFor the homogeneous cosmological plasma, adiabaticity gives the cosmological entropy conservation equationor equivalently $s{a}^3=\text{constant}$ in a comoving volume.

If a relativistic species decouples when the coupled plasma has $g_{\ast s,\mathrm{dec}}$ entropy degrees of freedom, then after the plasma reaches $g_{\ast s}$ degrees of freedom,The ratio follows from separate redshifting of the decoupled species and cosmological entropy conservation in the coupled plasma.