Gravitational lensing statistics with extragalactic surveys III. Joint constraints on lambda(0) and Omega(0) from lensing statistics and the m-z relation for type Ia supernovae

I present constraints on cosmological parameters in the lambda(0)-Omega(0) plane from a joint analysis of gravitational lensing statistics (Helbig et al. 1999b) and the magnitude-redshift relation for Type Ia supernovae (Perlmutter et al. 1999; Riess et al. 1998). 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 lambda(0) and Omega(0) 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 lambda(0) - Omega(0). At 95% confidence, the upper limit on lambda(0) - Omega(0) 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 lambda(0) - Omega(0) is in the range .55-0.60 (again depending on the data set). For a flat universe with lambda(0) + Omega(2) = 1, this corresponds to upper limits on lambda(0), 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 lambda(0) approximate to 0.7 and Omega(0) approximate to 0.3 and is consistent with a flat universe but, neglecting other cosmological tests, does riot require it