Observational Constraints on General Relativistic Energy Conditions, Cosmic Matter Density and Dark Energy from X-Ray Clusters of Galaxies and Type-Ia Supernovae

New observational constraints on the cosmic matter density $\Omega_m$ and an effectively redshift-independent equation of state parameter $w_x$ of the dark energy are obtained while simultaneously testing the strong and null energy conditions of general relativity on macroscopic scales. The combination of REFLEX X-ray cluster and type-Ia supernova data shows that for a flat Universe the strong energy condition might presently be violated whereas the null energy condition seems to be fulfilled. This provides another observational argument for the present accelerated cosmic expansion and the absence of exotic physical phenomena related to a broken null energy condition. The marginalization of the likelihood distributions is performed in a manner to include a large fraction of the recently discussed possible systematic errors involved in the application of X-ray clusters as cosmological probes. This yields for a flat Universe, $\Omega_m=0.29^{+0.08}_{-0.12}$ and $w_x=-0.95^{+0.30}_{-0.35}$ ($1\sigma$ errors without cosmic variance). The scatter in the different analyses indicates a quite robust result around $w_x=-1$, leaving little room for the introduction of new energy components described by quintessence-like models or phantom energy. The most natural interpretation of the data is a positive cosmological constant with $w_x=-1