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