Studying light propagation in a locally homogeneous universe through an
  extended Dyer-Roeder approach
  Light is affected by local inhomogeneities in its propagation, which may
alter distances and so cosmological parameter estimation. In the era of
precision cosmology, the presence of inhomogeneities may induce systematic
errors if not properly accounted. In this vein, a new interpretation of the
conventional Dyer-Roeder (DR) approach by allowing light received from distant
sources to travel in regions denser than average is proposed. It is argued that
the existence of a distribution of small and moderate cosmic voids (or "black
regions") implies that its matter content was redistributed to the homogeneous
and clustered matter components with the former becoming denser than the cosmic
average in the absence of voids. Phenomenologically, this means that the DR
smoothness parameter (denoted here by $\alpha_E$) can be greater than unity,
and, therefore, all previous analyses constraining it should be rediscussed
with a free upper limit. Accordingly, by performing a statistical analysis
involving 557 type Ia supernovae (SNe Ia) from Union2 compilation data in a
flat $\Lambda$CDM model we obtain for the extended parameter,
$\alpha_E=1.26^{+0.68}_{-0.54}$ ($1\sigma$). The effects of $\alpha_E$ are also
analyzed for generic $\Lambda$CDM models and flat XCDM cosmologies. For both
models, we find that a value of $\alpha_E$ greater than unity is able to
harmonize SNe Ia and cosmic microwave background observations thereby
alleviating the well-known tension between low and high redshift data. Finally,
a simple toy model based on the existence of cosmic voids is proposed in order
to justify why $\alpha_E$ can be greater than unity as required by supernovae
data.
