  Using molecular dynamics simulations we examine the system size dependence of
the fast dynamics in two model glass forming liquids, one of them a
Lennard-Jones mixture for which cooperative fast relaxation has been reported.
We find no indication of a temperature-dependent dynamic length scale
characterizing these fast dynamics; the size effects in the short time range
are temperature independent, and the consequence of cutting off of long
wavelength acoustic modes. In a molecular liquid exhibiting a clear
Johari-Goldstein (JG) relaxation, significant size effects are again present
both for the vibrational motion and long-time {\alpha} relaxation (only the
latter having a significant temperature dependence), but absent for the JG
relaxation.
