Luminous Cluster Ellipticals as Cosmological Standard Rods?

We explore the possibility to calibrate massive cluster ellipticals as cosmological standard rods. The method is based on the Fundamental Plane relation combined with a correction for luminosity evolution which is derived from the Mg$-\sigma$ relation. Principle caveats and sources of major errors are briefly discussed. We apply the described procedure to nine elliptical galaxies in two clusters at $z=0.375$ and derive constraints on the cosmological model. For the best fitting $\Lambda$-free cosmological model we obtain: $q_o \approx 0.1$, with 90% confidence limits being $0 < q_o < 0.7$ (the lower limit being due to the presence of matter in the Universe). If the inflationary scenario applies (i.e., space has flat geometry), then, for the best fitting model, matter and $\Lambda$ contribute about equally to the critical cosmic density (i.e. $\Omega_m \approx \Omega_\Lambda \approx 0.5$). With 90% confidence $\Omega_\Lambda$ should be smaller than 0.9.