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

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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.