Gravitational lensing statistics with extragalactic surveys. III. Joint constraints on lambda0 and Omega0 from lensing statistics and the m-z relation for type Ia supernovae
Abstract
I present constraints on cosmological parameters in the lambda0-Omega0 plane from a joint analysis of gravitational lensing statistics (astro-ph/9904175) and the magnitude-redshift relation for Type Ia supernovae (astro-ph/9812133 and astro-ph/9805201). I discuss reasons why this particular combination of tests is important and how the constraints can be improved in the future. The lensing statistics and supernova results are not inconsistent, thus it is meaningful to determine joint constraints on lambda0 and Omega0 by combining the results from both tests. The quantity measured by the lens statistics and the m-z relation for type Ia supernovae discussed here is approximately lambda0 - Omega0. At 95% confidence, the upper limit on lambda0 - Omega0 from lensing statistics alone is 0.45 and from supernovae alone is in the range 0.65--0.81 (depending on the data set). For joint constraints, the upper limit on lambda0 - Omega0 is in the range 0.55--0.60 (again depending on the data set). For a flat universe with lambda0 + Omega0 = 1, this corresponds to upper limits on lambda0, taking the top of the range from different data sets, of 0.72, 0.90 and 0.80 for lensing statistics alone, supernovae alone and the joint analysis, respectively. This is perfectly consistent with the current `standard cosmological model' with lambda0 approximately 0.7 and Omega0 approximately 0.3 and is consistent with a flat universe but, neglecting other cosmological tests, does not require it.
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