I present constraints on cosmological parameters in the \lambda _ { 0 } - \Omega _ { 0 } plane from a joint analysis of gravitational lensing statistics ( 13 ) and the magnitude-redshift relation for Type Ia supernovae ( 21 ; 23 ) .
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 0.55–0.60 ( again depending on the data set ) .
For a flat universe with \lambda _ { 0 } + \Omega _ { 0 } = 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 } \approx 0.7 and \Omega _ { 0 } \approx 0.3 and is consistent with a flat universe but , neglecting other cosmological tests , does not require it .