Bounding the Hubble flow in terms of the w parameter

TL;DR

This paper investigates how constraints on the w-parameter, representing the cosmological equation of state, can provide refined bounds on the Hubble flow and related cosmological quantities across different curvature scenarios.

Contribution

It systematically explores the impact of w-parameter constraints on the Hubble flow for arbitrary curvature, extending previous partial results with comprehensive calculations.

Findings

Derived bounds on density rho(z) and Hubble parameter H(z)

Established relationships between w-parameter constraints and cosmological distances d(z)

Analyzed effects for arbitrary curvature k in [-1,0,+1]

Abstract

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.