Investigating the redshift evolution of lensing galaxy density slopes via model-independent distance ratios

Context. Strong-lensing systems are expected to be discovered in great numbers by next-generation surveys. They provide a powerful tool for studying cosmology and the galaxy evolution. The coupling of the galaxy structure and cosmology through distance ratios means that it is essential for advancing both fields to examine the evolution of the lensing galaxy mass density profiles. Aims. We introduce a novel method that is independent of the dark energy assumed in the model to investigate the mass density slopes of lensing galaxies and their redshift evolution using an extended power-law (EPL) model. Methods. We adopted a nonparametric approach based on artificial neural networks trained on type Ia supernovae data to reconstruct the distance ratios of strong-lensing systems. These reconstructed ratios were compared with theoretical predictions to estimate the evolution of EPL model parameters. Results. A negative evolutionary trend of the mass density power-law exponent with increasing redshift is observed across different analysis levels. Assuming a triangular prior for the anisotropy of lensing galaxies, we find evidence for a redshift evolution of the mass density slope, quantified as ∂γ/∂z = −0.20 ± 0.12. Conclusions. This study confirms that the redshift evolution of the matter density slopes in lensing galaxies can be determined independent of dark energy models at the population level. The Legacy Survey of Space and Time (LSST) Rubin Observatory forecasts are expected to identify 100 000 strongly lensed galaxies. We show based on simulations with data from the LSST that spectroscopic follow up of just 10% of these systems can reduce the uncertainty in the redshift evolution coefficient of the total mass density slope (Δ∂γ/∂z) to 0.021. This precision would be able to distinguish between evolving and nonevolving scenarios for lensing galaxies.