Probing the cosmic distance duality with strong gravitational lensing and supernovae la data

We propose and perform a new test of the cosmic distance-duality relation (CDDR), D-L(z)/D-A(z)(1 vertical bar z)(2) = 1, where D-A is the angular diameter distance and D-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-A12/D-A2 and D* = D-L12/D-L2, where the subscripts 1 and 2 correspond, respectively, to redshifts z(1) and z(2), are linked by D/D* = (1+z(1))(2) if the CDDR is valid. We allow departures from the CDDR by defining two functions for eta(z(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 l sigma confidence level (eta(z) similar or equal to 1), in complete agreement with other tests and reinforcing the theoretical pillars of the CDDR.