Supernovae as probes of cosmic parameters: estimating the bias from under-dense lines of sight

Abstract

Correctly interpreting observations of sources such as type Ia supernovae (SNe Ia) require knowledge of the power spectrum of matter on AU scales - which is very hard to model accurately. Because under-dense regions account for much of the volume of the universe, light from a typical source probes a mean density significantly below the cosmic mean. The relative sparsity of sources implies that there could be a significant bias when inferring distances of SNe Ia, and consequently a bias in cosmological parameter estimation. While the weak lensing approximation should in principle give the correct prediction for this, linear perturbation theory predicts an effectively infinite variance in the convergence for ultra-narrow beams. We attempt to quantify the effect typically under-dense lines of sight might have in parameter estimation by considering three alternative methods for estimating distances, in addition to the usual weak lensing approximation. We find in each case this not only increases the errors in the inferred density parameters, but also introduces a bias in the posterior value.