The magnitude-redshift relation for type Ia supernovae, locally inhomogeneous cosmological models, and the nature of dark matter

The magnitude-distance relation for Type~Ia supernovae is one of the key pieces of evidence supporting the cosmological concordance model. The resulting constraints on the cosmological parameters are often derived under the idealized assumption that the universe is perfectly homogeneous on small scales. Since we know that this is not the case, what does this mean for constraints on cosmological parameters derived from the magnitude-distance relation for Type~Ia supernovae? And, conversely, what does the fact that these constraints, when small-scale homogeneity is assumed, agree with other constraints mean for the nature of dark matter?