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

We conduct the cosmological analysis by using the lens-redshift distribution test with updated galaxy-scale strong lensing sample, where the considered scenarios 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-dispersion distribution function (VDF) of lens galaxies. It shows that degeneracies between cosmological and VDF parameters lead to the shifts of estimates on the parameters. The limits on $\Omega_{m0}$ from the lens-redshift distribution are consistent with those from the Pantheon+ Type Ia supernova (SN Ia) sample at 68.3% confidence level, though the uncertainties on $\Omega_{m0}$ from the former are about 3 to 8 times larger than those from the latter. The mean values of $\Omega_{m0}$ shift to the larger values in the power-law VDF case and to the lower values in the exponential VDF case, compared with those obtained 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 with those from the Pantheon+ sample at 68.3% confidence level, but the mean values of $\omega_0$ from the former are significantly smaller than those from the latter. In the $\omega_0\omega_a$CDM model, the uncertainties on $\omega_0$ are dramatically 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-redshift distribution test is more effective on constraining $\Omega_{m0}$ than on the dark energy EoS.