  A recently proposed scenario for baryogenesis, called post--sphaleron
baryogenesis (PSB) is discussed within a class of quark--lepton unified
framework based on the gauge symmetry SU(2)_L x SU(2)_R x SU(4)_c realized in
the multi--TeV scale. The baryon asymmetry of the universe in this model is
produced below the electroweak phase transition temperature after the
sphalerons have decoupled from the Hubble expansion. These models embed
naturally the seesaw mechanism for neutrino masses, and predict color-sextet
scalar particles in the TeV range which may be accessible to the LHC
experiments. A necessary consequence of this scenario is the baryon number
violating \Delta B=2 process of neutron--antineutron (n-\bar{n}) oscillations.
In this paper we show that the constraints of PSB, when combined with the
neutrino oscillation data and restrictions from flavor changing neutral
currents mediated by the colored scalars imply an upper limit on the n-\bar{n}
oscillation time of 5 x 10^{10} sec. regardless of the quark--lepton
unification scale. If this scale is relatively low, in the (200-250) TeV range,
\tau_{n-\bar{n}} is predicted to be less than 10^{10} sec., which is accessible
to the next generation of proposed experiments.
