An improved method to test the Distance--Duality relation
  Many researchers have performed cosmological-model-independent tests for the
distance duality (DD) relation. Theoretical work has been conducted based on
the results of these tests. However, we find that almost all of these tests
were perhaps not cosmological-model-independent after all, because the distance
moduli taken from a given type Ia supernovae (SNe Ia) compilation are dependent
on a given cosmological model and Hubble constant. In this Letter, we overcome
these defects and by creating a new cosmological-model-independent test for the
DD relation. We use the original data from the Union2 SNe Ia compilation and
the angular diameter distances from two galaxy cluster samples compiled by De
Filippis et al. and Bonamente et al. to test the DD relation. Our results
suggest that the DD relation is compatible with observations, and the spherical
model is slightly better than the elliptical model at describing the intrinsic
shape of galaxy clusters if the DD relation is valid. However, these results
are different from those of previous work.
