Revisiting the effect of lens mass models in cosmological applications of strong gravitational lensing

Strong gravitational lens system catalogues are typically used to constrain a combination of cosmological and empirical power-law lens mass model parameters, often introducing additional empirical parameters and constraints from high resolution imagery. We investigate these lens models using Bayesian methods through a novel alternative that treats spatial curvature via the non-FLRW timescape cosmology. We apply Markov Chain Monte Carlo methods using the catalogue of 161 lens systems of Chen et al., in order to constrain both lens and cosmological parameters for: (i) the standard $\Lambda$CDM model with zero spatial curvature; and (ii) the timescape model. We then generate large mock data sets to further investigate the choice of cosmology on fitting simple power-law lens models. In agreement with previous results, we find that in combination with single isothermal sphere parameters, models with zero FLRW spatial curvature fit better as the free parameter approaches an unphysical empty universe, $\Omega _{\mathrm{M}0}\rightarrow 0$. By contrast, the timescape cosmology is found to prefer parameter values in which its cosmological parameter, the present void fraction, is driven to $f_{\mathrm{v}0}\rightarrow 0.73$ and closely matches values that best fit independent cosmological data sets: supernovae Ia distances and the cosmic microwave background. This conclusion holds for a large range of seed values $f_{\mathrm{v}0}\in \lbrace 0.1,0.9\rbrace$, and for timescape fits to both timescape and FLRW mocks. Regardless of cosmology, unphysical estimates of the distance ratios given from power-law lens models result in poor goodness of fit. With larger data sets soon available, separation of cosmology and lens models must be addressed.