TDCOSMO VI: Distance Measurements in Time-delay Cosmography under the Mass-sheet transformation

TL;DR

This paper demonstrates a method to break the mass-sheet degeneracy in time-delay cosmography without assuming a specific cosmological model, enabling more independent measurements of the Hubble constant.

Contribution

It introduces a novel approach combining lensing with supernovae and BAO data to constrain the distance ratio independently of cosmological assumptions.

Findings

Mass-sheet degeneracy can be broken without assuming a cosmological model.

Model-independent distance measurements in time-delay cosmography are feasible.

The method enhances the robustness of H0 measurements from gravitational lensing.

Abstract

Time-delay cosmography with gravitationally lensed quasars plays an important role in anchoring the absolute distance scale and hence measuring the Hubble constant, $H_{0}$, independent of traditional distance ladder methodology. A current potential limitation of time delay distance measurements is the "mass-sheet transformation" (MST) which leaves the lensed imaging unchanged but changes the distance measurements and the derived value of $H_0$. In this work we show that the standard method of addressing the MST in time delay cosmography, through a combination of high-resolution imaging and the measurement of the stellar velocity dispersion of the lensing galaxy, depends on the assumption that the ratio, $D_{\rm s}/D_{\rm ds}$, of angular diameter distances to the background quasar and between the lensing galaxy and the quasar can be constrained. This is typically achieved through the assumption of a particular cosmological model. Previous work (TDCOSMO IV) addressed the mass-sheet degeneracy and derived $H_{0}$ under the assumption of $\Lambda$CDM model. In this paper we show that the mass sheet degeneracy can be broken without relying on a specific cosmological model by combining lensing with relative distance indicators such as supernovae type Ia and baryon acoustic oscillations, which constrain the shape of the expansion history and hence $D_{\rm s}/D_{\rm ds}$. With this approach, we demonstrate that the mass-sheet degeneracy can be constrained in a cosmological-model-independent way, and hence model-independent distance measurements in time-delay cosmography under mass-sheet transformations can be obtained.