Cosmic distance duality relation and the shape of galaxy clusters

Context. Observations in the cosmological domain are heavily dependent on the validity of the cosmic distance-duality (DD) relation, η = DL(z)(1 + z)2/DA(z) = 1, an exact result required by the Etherington reciprocity theorem where DL(z) and DA(z) are, respectively, the luminosity and angular diameter distances. In the limit of very small redshifts DA(z) = DL(z) and this ratio is trivially satisfied. Measurements of Sunyaev-Zeldovich effect (SZE) and X-rays combined with the DD relation have been used to determine DA(z) from galaxy clusters. This combination offers the possibility of testing the validity of the DD relation, as well as determining which physical processes occur in galaxy clusters via their shapes.