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

Abstract

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.

11 pages, 17 figures, published in Monthly Notices of the Royal Astronomical Society. This version contains minor changes made while correcting proofs in order to correspond as closely as practical to the offical version. No changes in content. Related information available at http://www.astro.multivax.de:8000/helbig/research/publications/info/etasnia.html

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• Type Ia supernova constraints on compact object dark matter
• The Effect of Gravitational Lensing on Fast Transient Event Rates
• The $m$-$z$ relation for Type Ia supernovae: safety in numbers or safely without worry?
• Line of sight paraxial gravitational cloaking