Swiss-cheese models and the Dyer-Roeder approximation
  In view of interpreting the cosmological observations precisely, especially
when they involve narrow light beams, it is crucial to understand how light
propagates in our statistically homogeneous, clumpy, Universe. Among the
various approaches to tackle this issue, Swiss-cheese models propose an
inhomogeneous spacetime geometry which is an exact solution of Einstein's
equation, while the Dyer-Roeder approximation deals with inhomogeneity in an
effective way. In this article, we demonstrate that the distance-redshift
relation of a certain class of Swiss-cheese models is the same as the one
predicted by the Dyer-Roeder approach, at a well-controlled level of
approximation. Both methods are therefore equivalent when applied to the
interpretation of, e.g., supernova observations. The proof relies on completely
analytical arguments, and is illustrated by numerical results.
