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#### TDCOSMO - VI. Distance measurements in time-delay cosmography under the mass-sheet transformation

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##### Citation

Chen, G.-C.-F., Fassnacht, C. D., Suyu, S. H., Yildirim, A., Komatsu, E., & Bernal, J. L. (2021).
TDCOSMO - VI. Distance measurements in time-delay cosmography under the mass-sheet transformation.*
Astronomy and Astrophysics,* *652*: A7. doi:10.1051/0004-6361/202039895.

Cite as: http://hdl.handle.net/21.11116/0000-0009-5F96-4

##### 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_{s}/D_{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 the ΛCDM 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_{s}/D_{ds}. With this approach, we demonstrate that the mass-sheet degeneracy can be constrained in a cosmological model-independent way. Hence model-independent distance measurements in time-delay cosmography under MSTs can be obtained.