Utilizing the CLASS statistical sample , we investigate the constraint of the splitting angle statistic of strong gravitational lenses ( SGL ) on the equation-of-state parameter w = p / \rho of the dark energy in the flat cold dark matter cosmology .
Through the comoving number density of dark halos described by Press-Schechter theory , dark energy affects the efficiency with which dark-matter concentrations produce strong lensing signals .
The constraints on both constant w and time-varying w ( z ) = w _ { 0 } + w _ { a } z / ( 1 + z ) from the SGL splitting angle statistic are consistently obtained by adopting a two model combined mechanism of dark halo density profile matched at the mass scale M _ { c } .
Our main observations are : ( a ) the resulting model parameter M _ { c } is found to be M _ { c } \sim 1.4 for both constant w and time-varying w ( z ) , which is larger than M _ { c } \sim 1 obtained in literatures ; ( b ) the fitting results for the constant w are found to be w = -0.89 ^ { +0.49 } _ { -0.26 } and w = -0.94 ^ { +0.57 } _ { -0.16 } for the source redshift distributions of the Gaussian models g ( z _ { s } ) and g ^ { c } ( z _ { s } ) respectively , which are consistent with the \Lambda CDM at 95 % C.L ; ( c ) the time-varying w ( z ) is found to be for \sigma _ { 8 } = 0.74 : ( M _ { c } ;w _ { 0 } ,w _ { a } ) = ( 1.36 ; -0.92 , -1.31 ) and ( M _ { c } ;w _ { 0 } ,w _ { a } ) = ( 1.38 ; -0.89 , -1.21 ) for g ( z _ { s } ) and g ^ { c } ( z _ { s } ) respectively , the influence of \sigma _ { 8 } is investigated and found to be sizable for \sigma _ { 8 } = 0.74 \sim 0.90 .
After marginalizing the likelihood functions over the cosmological parameters ( \Omega _ { M } ,h, \sigma _ { 8 } ) and the model parameter M _ { c } , we find that the data of SGL splitting angle statistic lead to the best fit results ( w _ { 0 } ,w _ { a } ) = ( -0.88 ^ { +0.65 } _ { -1.03 } , -1.55 ^ { +1.77 } _ { -1.88 } ) and ( w _ { 0 } ,w _ { a } ) = ( -0.91 ^ { +0.60 } _ { -1.46 } , -1.60 ^ { +1.60 } _ { -2.57 } ) for g ( z _ { s } ) and g ^ { c } ( z _ { s } ) respectively .