$t < 1$ s In equilibrium
• $T > 1$ MeV: weak reactions \[\large \nu\bar\nu \leftrightarrow e^+e^-, \qquad \nu e \leftrightarrow \nu e\]
• Keep neutrinos thermal with everything else
$t \approx 1$ s Freeze-out
• $\Gamma \sim G_F^2 T^5$ falls below $H \sim T^2/M_{\rm Pl}$
• Neutrinos decouple and free-stream ever after
$t \gtrsim$ few s Cosmic $\nu$ background
• $e^+e^-$ annihilation heats only the photons: \[\large T_\nu = (4/11)^{1/3}\, T_\gamma\]
• Today: $T_\nu \approx 1.95$ K, $\sim$340 cm$^{-3}$
• $\nu$: never touched again, but felt by gravity
• 40% of the radiation, speed up the expansion
• Expansion rate counts species: $N_{\rm eff}$
$t \approx 3$ min Light elements (BBN)
• $\nu_e$ swap $n \leftrightarrow p$ until 1 s
• By 3 min, $n/p \approx 1/7$
• Nearly all neutrons $\to$ $^4$He: 25% by mass
• More species, faster expansion, more He
• Limitted in 1977, before LEP found 3
$\gtrsim 10^8$ yr Stars
• Two $\nu_e$ per $^4$He made
• The Sun emits $2\times10^{38}$ $\nu$/s
• 65 billion cross your thumbnail each second
• Super-K sees only $^8$B: 1 in $10^4$
Core collapse Supernovae
• 99% of energy leaves as $10^{58}$ neutrinos in $\sim$10 s
Also Everything else
• Earth's radioactivity, reactors
• Cosmic-ray showers
• Cosmic accelerators (TeV–PeV)