Cosmodynamics: energy conditions, Hubble bounds, density bounds, time and distance bounds

We refine and extend a programme initiated by one of the current authors (Visser 1997 Science 276 88, Visser 1997 Phys. Rev. D 56 7578) advocating the use of the classical energy conditions of general relativity in a cosmological setting to place very general and robust bounds on various cosmological parameters. We show how the energy conditions can be used to bound the Hubble parameter H(z), Omega parameter Ω(z), density ρ(z), distance d(z) and lookback time T(z) as (relatively) simple functions of the redshift z, present-epoch Hubble parameter H₀ and present-epoch Omega parameter Ω₀. The bounds we obtain are typically in the form of polynomial, rational, algebraic or elementary functions, and only in one specific case do we need to deal with special functions (the hypergeometric function). We compare these results with related observations in the literature, in several cases developing new and considerably more general bounds, and then confront these bounds with the recent supernova data.