Based on the latest SNe Ia data provided by Hicken et al .
( 2009 ) with using MLCS17 light curve fitter , together with the Baryon Acoustic Oscillation ( BAO ) and strong gravitational lenses ( SGL ) , we investigate the constraints on the dark energy equation-of-state parameter w in the flat universe , especially for the time-varying case w ( z ) = w _ { 0 } + w _ { z } z / ( 1 + z ) .
The constraints from SNe data alone are found to be : ( a ) ( \Omega _ { M } ,w ) = ( 0.358 , -1.09 ) as the best-fit results ; ( b ) ( w _ { 0 } ,w _ { z } ) = ( -0.73 ^ { +0.23 } _ { -0.97 } , 0.84 ^ { +1.66 } _ { -10.34 } ) for the two parameters in the time-varying case after marginalizing the parameter \Omega _ { M } ; ( c ) the likelihood of parameter w _ { z } has a high non-Gaussian distribution ; ( d ) an extra restriction on \Omega _ { M } is necessary to improve the constraint of the SNe Ia data on the parameters ( w _ { 0 } , w _ { z } ) .
A joint analysis of SNe Ia data and BAO is made to break the degeneracy between w and \Omega _ { M } , and leads to the interesting maximum likelihoods w _ { 0 } = -0.94 and w _ { z } = 0 .
When marginalizing the parameter \Omega _ { M } , the fitting results are found to be ( w _ { 0 } ,w _ { z } ) = ( -0.95 ^ { +0.45 } _ { -0.18 } , 0.41 ^ { +0.79 } _ { -0.96 } ) .
After adding the splitting angle statistic of SGL data , a consistent constraint is obtained ( \Omega _ { M } ,w ) = ( 0.298 , -0.907 ) and the constraints on time-varying dark energy are further improved to be ( w _ { 0 } ,w _ { z } ) = ( -0.92 ^ { +0.14 } _ { -0.10 } , 0.35 ^ { +0.47 } _ { -0.54 } ) , which indicates that the phantom type models are disfavored .