Strongly gravitational lensed SNe Ia as multi-messengers: Direct test of the Friedmann-Lema\^{\i}tre-Robertson-Walker metric

Abstract

We present a new idea of testing the validity of the Friedman-Lema\^{\i}tre-Robertson-Walker metric, through the multiple measurements of galactic-scale strong gravitational lensing systems with type Ia supernovae in the role of sources. Each individual lensing system will provide a model-independent measurement of the spatial curvature parameter referring only to geometrical optics independently of the matter content of the universe. This will create a valuable opportunity to test the FLRW metric directly. Our results show that with hundreds of strongly lensed SNe Ia observed by LSST, one would produce robust constraints on the spatial curvature with accuracy $\Delta \Omega_k=0.04$ comparable to the Planck 2015 results.