In this letter , we present a new determination of the local ( z \leq 0.09 ) X-ray luminosity function ( XLF ) using a large , statistical sample of 294 Abell clusters and the ROSAT All-Sky-Survey .
Despite the optical selection of this catalog , we find excellent agreement with other recent determinations of the local XLF .
Given our large sample size , we have reduced errors by \approx a factor of two for L _ { X ( 0.5 - 2.0 ~ { } keV ) } \geq 10 ^ { 43 } h _ { 50 } ^ { -2 } ~ { } ergs / sec .
We combine our data with previous work to produce the most tightly constrained local determination of the XLF over three orders of magnitude in L _ { X } in order to explore possible constraints imposed by the shape of the XLF on cosmological models .
A set of currently viable cosmologies is used to construct theoretical XLFs assuming L \propto M ^ { p } and a \sigma _ { 8 } - \Omega _ { 0 } constraint ( from Viana & Liddle 1996 ) based on the local X-ray temperature function .
We fit these models to our observed XLF and verify that the simplest adiabatic , analytic scaling relation ( e.g . Kaiser 1986 ) disagrees strongly with observations .
If we assume that clusters can be described by the pre-heated , constant core entropy models of Evrard & Henry ( 1991 ) then the observed XLF is consistent only with 0.1 < \Omega _ { 0 } < 0.4 if the energy per unit mass in galaxies is roughly equal to the gas energy ( i.e. , if \beta \sim 1 ) .