Inverse-Compton cooling time

What you are seeing: the Thomson-limit IC cooling time $t_\text{cool} = 3 m_e c / (4 \sigma_T \gamma U_\text{ph})$ plotted versus electron Lorentz factor $\gamma$, with the soft-photon energy density $U_\text{ph}$ set by a thermal bath of temperature $T$. For CMB ($T = 2.725$ K, $U_\text{CMB} \approx 4.2 \times 10^{-14}$ J/m$^3$), a $\gamma = 10^5$ electron cools in tens of Myr.

Cosmic ray electrons above $\gamma \sim 10^7$ ($E \sim 5$ TeV) cool on Galactic-disk crossing times; this sets the local TeV electron population and the cosmic-ray "knee" near 1 PeV. The dashed line marks the Hubble time as a reference.