The $m$-$z$ relation for type Ia supernovae, locally inhomogeneous
  cosmological models, and the nature of dark matter
  The $m$-$z$ relation for type Ia supernovae is one of the key pieces of
evidence supporting the cosmological `concordance model' with $\lambda_0
\approx 0.7$ and $\Omega_0 \approx 0.3$. However, it is well known that the
$m$-$z$ relation depends not only on $\lambda_0$ and $\Omega_0$ (with $H_0$ as
a scale factor) but also on the density of matter along the line of sight,
which is not necessarily the same as the large-scale density. I investigate to
what extent the measurement of $\lambda_0$ and $\Omega_0$ depends on this
density when it is characterized by the parameter $\eta$ ($0 \le \eta \le 1$),
which describes the ratio of density along the line of sight to the overall
density. I also discuss what constraints can be placed on $\eta$, both with and
without constraints on $\lambda_0$ and $\Omega_0$ in addition to those from the
$m$-$z$ relation for type~Ia supernovae.
