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We propose and perform a new test of the cosmic distance-duality relation (CDDR), DL (z) / DA (z) (1 + z) ^2 = 1, where DA is the angular diameter distance and DL 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=D₀_₁₂/D₀䃒 and D^*=D₋_₁₂/D₋_₂, where the subscripts 1 and 2 correspond, respectively, to redshifts z₁ and z₂, are linked by D/D^*= (1+z₁) ² if the CDDR is valid. We allow departures from the CDDR by defining two funcions for (z₁), 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 1 confidence level ( (z) 1), in complete agreement with other tests and reinforcing the theoretical pillars of the CDDR.
Holanda et al. (Mon,) studied this question.