The weak energy condition and the expansion history of the Universe

We examine flat models containing a dark matter component and an arbitrary dark energy component, subject only to the constraint that the dark energy satisfies the weak energy condition. We determine the constraints that these conditions place on the evolution of the Hubble parameter with redshift, H(z)$H(z)$, and on the scaling of the coordinate distance with redshift, r(z)$r(z)$. Observational constraints on H(z)$H(z)$ are used to derive an upper bound on the current matter density. We demonstrate how the weak energy condition constrains fitting functions for r(z)$r(z)$.