  We study the relaxation dynamics of the one-dimensional Tomonaga-Luttinger
model after an interaction quench paying particular attention to the momentum
dependence of the two-particle interaction. Several potentials of different
analytical form are investigated all leading to universal Luttinger liquid
physics in equilibrium. The steady-state fermionic momentum distribution shows
universal behavior in the sense of the Luttinger liquid phenomenology. For
generic regular potentials the large time decay of the momentum distribution
function towards the steady-state value is characterized by a power law with a
universal exponent which only depends on the potential at zero momentum
transfer. A commonly employed ad hoc procedure fails to give this exponent.
Besides quenches from zero to positive interactions we also consider abrupt
changes of the interaction between two arbitrary values. Additionally, we
discuss the appearance of a factor of two between the steady-state momentum
distribution function and the one obtained in equilibrium at equal two-particle
interaction.
