Strongly lensed gravitational waves as the probes to test the cosmic distance duality relation

Abstract

The cosmic distance relation (DDR) associates the angular diameters distance ($D_A$) and luminosity distance ($D_L$) by a simple formula, i.e., $D_L=(1+z{)}^2{D}_A$. The strongly lensed gravitational waves (GWs) provide a unique way to measure $D_A$ and $D_L$ simultaneously to the GW source, hence can be used as probes to test DDR. In this paper, we prospect the use of strongly lensed GW events from the future Einstein Telescope to test DDR. We write the possible deviation of DDR as $(1+z{)}^2{D}_A/D_L=\eta (z)$, and consider two different parametrizations of $\eta (z)$, namely, ${\eta }_1(z)=1+{\eta }_{0}z$ and ${\eta }_2(z)=1+{\eta }_{0}z/(1+z)$. Numerical simulations show that, with about 100 strongly lensed GW events observed by ET, the parameter ${\eta }_0$ can be constrained at $1.3\%$ and $3\%$ levels for the first and second parametrizations, respectively.

8 pages, 3 figures

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Cited by in corpus (9)

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• Machine learning forecasts of the cosmic distance duality relation with strongly lensed gravitational wave events
• The cosmic distance duality relation in light of the time-delayed strong gravitational lensing
• On the cosmic distance duality relation and the strong gravitational lens power law density profile
• Deep learning method in testing the cosmic distance duality relation
• Distance-duality in theories with a nonminimal coupling to gravity
• Fundamental Physics and Cosmology with TianQin
• The impact of 2D and 3D BAO measurements on the Cosmic Distance Duality Relation with HII galaxies
• Testing the Distance Duality Relation with Cosmological Observations at high Redshift using Artificial Neural Network