The central ambition of the modern time delay cosmography consists in determining the Hubble constant H0 with a competitive precision. However, the tension with H0 obtained from the Planck satellite ...for a spatially flat ΛCDM cosmology suggests that systematic errors may have been underestimated. The most critical of these errors probably comes from the degeneracy existing between lens models that was first formalized by the well-known mass-sheet transformation (MST). In this paper, we assess to what extent the source position transformation (SPT), a more general invariance transformation which contains the MST as a special case, may affect the time delays predicted by a model. To this aim, we have used pySPT, a new open-source python package fully dedicated to the SPT that we present in a companion paper. For axisymmetric lenses, we find that the time delay ratios between a model and its SPT-modified counterpart simply scale like the corresponding source position ratios, Δtˆ/Δt ≈ βˆ/β $\mathrm{\Delta} \hat{t}/ \mathrm{\Delta} t \approx \hat{\beta}/\beta$ Δt^/Δt≈β^/β , regardless of the mass profile and the isotropic SPT. Similar behavior (almost) holds for nonaxisymmetric lenses in the double image regime and for opposite image pairs in the quadruple image regime. In the latter regime, we also confirm that the time delay ratios are not conserved. In addition to the MST effects, the SPT-modified time delays deviate in general no more than a few percent for particular image pairs, suggesting that its impact on time delay cosmography seems not be as crucial as initially suspected. We also reflected upon the relevance of the SPT validity criterion and present arguments suggesting that it should be reconsidered. Even though a new validity criterion would affect the time delays in a different way, we expect from numerical simulations that our conclusions will remain unchanged.
Modern time-delay cosmography aims to infer the cosmological parameters with a competitive precision from observing a multiply imaged quasar. The success of this technique relies upon a robust ...modeling of the lens mass distribution. Unfortunately strong degeneracies between density profiles that lead to almost the same lensing observables may bias precise estimates of the Hubble constant. The source position transformation (SPT), which covers the well-known mass-sheet transformation (MST) as a special case, defines a new framework to investigate these degeneracies. In this paper, we present pySPT, a python package dedicated to the SPT. We describe how it can be used to evaluate the impact of the SPT on lensing observables. We review most of its capabilities and elaborate on key features that we used in a companion paper regarding SPT and time delays. The pySPT program also comes with a subpackage dedicated to simple lens modeling. This can be used to generate lensing related quantities for a wide variety of lens models independent of any SPT analysis. As a first practical application, we present a correction to the first estimate of the impact on time delays of the SPT, which has been experimentally found in a previous work between a softened power law and composite (baryons + dark matter) lenses. We find that the large deviations previously predicted have been overestimated because of a minor bug in the public lens modeling code lensmodel (v1.99), which is now fixed. We conclude that the predictions for the Hubble constant deviate by ∼7%, first and foremost as a consequence of an MST. The latest version of pySPT is available on Github, a software development platform, along with some tutorials to describe in detail how making the best use of pySPT.
The modern time-delay cosmography aims to infer the cosmological parameters with a competitive precision from observing a multiply imaged quasar. The success of this technique relies upon a robust ...modeling of the lens mass distribution. Unfortunately strong degeneracies between density profiles that lead to almost the same lensing observables may bias precise estimate for the Hubble constant. The source position transformation (SPT), which covers the well-known mass sheet transformation (MST) as a special case, defines a new framework to investigate these degeneracies. In this paper, we present pySPT, a Python package dedicated to the SPT. We describe how it can be used to evaluate the impact of the SPT on lensing observables. We review most of its capabilities and elaborate on key features that we used in a companion paper regarding SPT and time delays. pySPT also comes with a sub-package dedicated to simple lens modeling. It can be used to generate lensing related quantities for a wide variety of lens models, independently from any SPT analysis. As a first practical application, we present a correction to the first estimate of the impact on time delays of the SPT, which has been experimentally found in Schneider and Sluse (2013) between a softened power-law and a composite (baryons + dark matter) lenses. We find that the large deviations predicted in Schneider and Sluse (2014) have been overestimated due to a minor bug (now fixed) in the public lens modeling code lensmodel (v1.99). We conclude that the predictions for the Hubble constant deviate by \(\sim 7\)\%, first and foremost caused by an MST. The latest version of pySPT is available at https://github.com/owertz/pySPT. We also provide tutorials to describe in detail how making the best use of pySPT at https://github.com/owertz/pySPT_tutorials.
The central ambition of the modern time delay cosmography consists in determining the Hubble constant \(H_0\) with a competitive precision. However, the tension with \(H_0\) obtained from the Planck ...satellite for a spatially-flat \(\Lambda\)CDM cosmology suggests that systematic errors may have been underestimated. The most critical one probably comes from the degeneracy existing between lens models that was first formalized by the well-known mass-sheet transformation (MST). In this paper, we assess to what extent the source position transformation (SPT), a more general invariance transformation which contains the MST as a special case, may affect the time delays predicted by a model. To this aim we use pySPT, a new open-source python package fully dedicated to the SPT that we present in a companion paper. For axisymmetric lenses, we find that the time delay ratios between a model and its SPT-modified counterpart simply scale like the corresponding source position ratios, \(\Delta \hat{t}/ \Delta t \approx \hat{\beta}/\beta\), regardless of the mass profile and the isotropic SPT. Similar behavior (almost) holds for non-axisymmetric lenses in the double image regime and for opposite image pairs in the quadruple image regime. In the latter regime, we also confirm that the time delay ratios are not conserved. In addition to the MST effects, the SPT-modified time delays deviate in general no more than a few percent for particular image pairs, suggesting that its impact on time-delay cosmography seems not be as crucial as initially suspected. We also reflected upon the relevance of the SPT validity criterion and present arguments suggesting that it should be reconsidered. Even though a new validity criterion would affect the time delays in a different way, we expect from numerical simulations that our conclusions will remain unchanged.
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