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

Abstract

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=DA12/DA2 and D*=DL12/DL2, 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 functions for η(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 1σ confidence level (η(z) ≃ 1), in complete agreement with other tests and reinforcing the theoretical pillars of the CDDR.