The dynamics of a causal bulk viscous cosmological fluid filled flat consta
ntly decelerating noninflationary Robertson-Walker spacetime is considered.
The matter component of the Universe is assumed to satisfy a linear barotr
opic equation of state and the state equation of the small temperature Bolt
zmann gas. The resulting cosmological models satisfy the condition of small
ness of the viscous stress. The evolution of the relaxation time, temperatu
re, bulk viscosity coefficient and comoving entropy of the dissipative cosm
ological fluid are obtained by assuming several bulk viscosity coefficient-
relaxation time relations.