  We construct one-zone steady-state models of cosmic ray (CR) injection,
cooling, and escape over the entire dynamic range of the FIR-radio correlation
(FRC), from normal galaxies to starbursts, over the redshift interval 0 <= z <=
10. Normal galaxies with low star-formation rates become radio-faint at high z,
because Inverse Compton (IC) losses off the CMB cool CR electrons and positrons
rapidly, suppressing their nonthermal radio emission. However, we find that
this effect occurs at higher redshifts than previously expected, because
escape, bremsstrahlung, ionization, and starlight IC losses act to counter this
effect and preserve the radio luminosity of galaxies. The radio dimming of
star-forming galaxies at high z is not just a simple competition between
magnetic field energy density and the CMB energy density; the CMB must also
compete with every other loss process. We predict relations for the critical
redshift when radio emission is significantly suppressed compared to the z ~ 0
FRC as a function of star-formation rate per unit area. Additionally, we
provide a quantitative explanation for the relative radio brightness of some
high-z submillimeter galaxies. We show that at fixed star formation rate
surface density, galaxies with larger CR scale heights are radio bright with
respect to the FRC, because of weaker bremsstrahlung and ionization losses
compared to compact starbursts. We predict that these "puffy starbursts" should
have steeper radio spectra than compact galaxies with the same star-formation
rate surface density. We find that radio bright submillimeter galaxies alone
cannot explain the excess radio emission reported by ARCADE2, but they may
significantly enhance the diffuse radio background with respect to a naive
application of the z ~ 0 FRC.
