  We analyze Cooper pairing instabilities in strongly driven electron-phonon
systems. The light-induced non-equilibrium state of phonons results in a
simultaneous increase of the superconducting coupling constant and the electron
scattering. We demonstrate that the competition between these effects leads to
an enhanced superconducting transition temperature in a broad range of
parameters. Our results may explain the observed transient enhancement of
superconductivity in several classes of materials upon irradiation with high
intensity pulses of terahertz light, and may pave new ways for engineering
high-temperature light-induced superconducting states.
