  This paper investigates the distribution and implications of cosmic ray
electrons within the intergalactic medium (IGM). Utilizing a synthesis model of
the extragalactic background, we evolve the spectrum of Compton-included cosmic
rays. The energy density distribution of cosmic ray electrons peaks at redshift
$z \approx2$, and peaks in the $\sim$MeV range. The fractional contribution of
cosmic ray pressure to the general IGM pressure progressively increases toward
lower redshift. At mean density, the ratio of cosmic ray electron to thermal
pressure in the IGM $ P_{\rm CRe} / P_{\rm th}$ is 0.3% at $z=2$, rising to
1.0% at $z=1$, and 1.8% at $z=0.1$ (considering only the cosmic rays produced
locally by Compton scattering). We compute the linear Landau damping rate of
plasma oscillations in the IGM caused by the $\sim$MeV cosmic ray electrons,
and find it to be of order $\sim 10^{-6}\,\rm s^{-1}$ for wavenumbers
$1.2\lesssim ck/\omega_{\rm p}\lesssim 5$ at $z=2$ and mean density (where
$\omega_{\rm p}$ is the plasma frequency). This strongly affects the fate of
TeV $e^+e^-$ pair beams produced by blazars, which are potentially unstable to
oblique instabilities involving plasma oscillations with wavenumber
$ck/\omega_{\rm p}\approx\sec\theta$ ($\theta$ being the angle between the beam
and wave vector). Linear Landau damping is at least thousands of times faster
than either pair beam instability growth or collisional effects; it thus turns
off the pair beam instability except for modes with very small $\theta$
($ck/\omega_{\rm p}\rightarrow 1$, where linear Landau damping is kinematically
suppressed). This leaves open the question of whether the pair beam instability
is turned off entirely, or can still proceed via the small-$\theta$ modes.
