Probing the cosmic distance duality with strong gravitational lensing and supernovae Ia data
We propose and perform a new test of the cosmic distance-duality relation (CDDR), D{sub L}(z) / D{sub A}(z) (1 + z){sup 2} = 1, where D{sub A} is the angular diameter distance and D{sub L} is the luminosity distance to a given source at redshift z, using strong gravitational lensing (SGL) and type Ia Supernovae (SNe Ia) data. We show that the ratio D=D{sub A{sub 1{sub 2}}}/D{sub A{sub 2}} and D{sup *}=D{sub L{sub 1{sub 2}}}/D{sub L{sub 2}}, where the subscripts 1 and 2 correspond, respectively, to redshifts z{sub 1} and z{sub 2}, are linked by D/D{sup *}=(1+z{sub 1}){sup 2} if the CDDR is valid. We allow departures from the CDDR by defining two functions for η(z{sub 1}), which equals unity when the CDDR is valid. We find that combination of SGL and SNe Ia data favours no violation of the CDDR at 1σ confidence level (η(z) ≅ 1), in complete agreement with other tests and reinforcing the theoretical pillars of the CDDR.