CONSTRAINING DARK ENERGY FROM THE SPLITTING ANGLE STATISTIC OF STRONG GRAVITATIONAL LENSES

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 (CDM) cosmology. Through the comoving number density of dark halos described by the 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 a dark halo density profile matched at the mass scale M-c. Our main observations are that (1) the resulting model parameter M-c is found to be M-c similar to 1.4 for both constant w and time-varying w(z), which is larger than M-c similar to 1 obtained in literatures; (2) the fitting results for the constant w are found to be w = -0.89(-0.26)(+0.49) and w = -0.94(-0.16)(+0.57) 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.; (3) the time-varying w(z) is found to be 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) = 0.74-0.90. After marginalizing the likelihood functions over the cosmological parameters (Omega(M), h, sigma(8)) and the model parameter Mc, we find that the data of SGL splitting angle statistic lead to the best-fit results (w(0), w(a)) =(-0.88(-1.03)(+0.65),-1.55(-1.88)(+1.77)) and (w(0), w(a)) = (-0.91(-1.46)(+0.60),- 1.60(-2.57)+(1.60)) for g(z(s)) and g(c)(z(s)), respectively.