  The last decade has seen increasing efforts to circumscribe and bound the
cosmological Hubble flow in terms of model-independent constraints on the
cosmological fluid - such as, for instance, the classical energy conditions of
general relativity. Quite a bit can certainly be said in this regard, but much
more refined bounds can be obtained by placing more precise constraints (either
theoretical or observational) on the cosmological fluid. In particular, the use
of the w-parameter (w=p/rho) has become increasingly common as a surrogate for
trying to say something about the cosmological equation of state. Herein we
explore the extent to which a constraint on the w-parameter leads to useful and
nontrivial constraints on the Hubble flow, in terms of constraints on density
rho(z), Hubble parameter H(z), density parameter Omega(z), cosmological
distances d(z), and lookback time T(z). In contrast to other partial results in
the literature, we carry out the computations for arbitrary values of the space
curvature k in [-1,0,+1], equivalently for arbitrary Omega_0 <= 1.
