Bounding the Hubble flow in terms of the w parameter

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—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/ρ) 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 non-trivial constraints on the Hubble flow, in terms of constraints on density ρ(z), Hubble parameter H(z), density parameter Ω(z), cosmological distances d(z), and lookback time T(z). In contrast to the case for other partial results in the literature, the computations here are carried out for arbitrary values of the space curvature , or equivalently for arbitrary .