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The $m$-$z$ relation for type Ia supernovae is one of the key pieces ofevidence 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 $H_0$ asa 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 towhat extent the measurement of $\lambda_0$ and $\Omega_0$ depends on thisdensity 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 overalldensity. I also discuss what constraints can be placed on $\eta$, both with andwithout constraints on $\lambda_0$ and $\Omega_0$ in addition to those from the$m$-$z$ relation for type~Ia supernovae.

The $m$-$z$ relation for type Ia supernovae, locally inhomogeneous cosmological models, and the nature of dark matter