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We conduct the cosmological analysis by using the lens-redshift distributiontest with updated galaxy-scale strong lensing sample, where the consideredscenarios involve three typical cosmological models (i.e., $\Lambda$CDM,$\omega$CDM and $\omega_0\omega_a$CDM models) and three typical choices (i.e.,non-evolving, power-law and exponential forms) for the velocity-dispersiondistribution function (VDF) of lens galaxies. It shows that degeneraciesbetween cosmological and VDF parameters lead to the shifts of estimates on theparameters. The limits on $\Omega_{m0}$ from the lens-redshift distribution areconsistent with those from the Pantheon+ Type Ia supernova (SN Ia) sample at68.3% confidence level, though the uncertainties on $\Omega_{m0}$ from theformer are about 3 to 8 times larger than those from the latter. The meanvalues of $\Omega_{m0}$ shift to the larger values in the power-law VDF caseand to the lower values in the exponential VDF case, compared with thoseobtained in the non-evolving VDF case. In the $\omega$CDM model, the limits on$\omega_0$, i.e. the dark energy equation of state (EoS), are consistent withthose from the Pantheon+ sample at 68.3% confidence level, but the mean valuesof $\omega_0$ from the former are significantly smaller than those from thelatter. In the $\omega_0\omega_a$CDM model, the uncertainties on $\omega_0$ aredramatically enlarged compared with those obtained in the $\omega$CDM model;moreover, the Markov chains of $\omega_a$, i.e. the time-varying slope of EoS,do not achieve convergence in the three VDF cases. Overall, the lens-redshiftdistribution test is more effective on constraining $\Omega_{m0}$ than on thedark energy EoS.

Cosmological application of the lens-redshift probability distribution with improved galaxy-scale gravitational lensing sample