  We show that the single-particle spectral properties of gapless
one-dimensional Fermi systems in the Luttinger liquid state reached at
intermediate times after an abrupt quench of the two-particle interaction are
highly indicative of the unusual nonequilibrium nature of this state. The line
shapes of the momentum integrated and resolved spectral functions strongly
differ from their ground state as well as finite temperature equilibrium
counterparts. Using an energy resolution improved version of radio-frequency
spectroscopy of quasi one-dimensional cold Fermi gases it should be possible to
experimentally identify this nonequilibrium state by its pronounced spectral
signatures.
