  An important part of cosmological model fitting relies on correlating
distance indicators of objects (for example type Ia supernovae) with their
redshift, often illustrated on a Hubble diagram. Comparing the observed
correlation with a homogeneous model is one of the key pieces of evidence for
dark energy. The presence of cosmic structures introduces a bias and scatter,
mainly due to gravitational lensing and peculiar velocities, but also due to
smaller non-linear relativistic contributions which are more difficult to
account for. For the first time we perform ray tracing onto halos in a
relativistic N-body simulation. Our simulation is the largest that takes into
account all leading-order corrections from general relativity in the evolution
of structure, and we present a novel methodology for working out the non-linear
projection of that structure onto the observer's past light cone. We show that
the mean of the bias in the Hubble diagram is indeed as small as expected from
perturbation theory. However, the distribution of sources is significantly
skewed with a very long tail of highly magnified objects and we illustrate that
the bias of cosmological parameters strongly depends on the function of
distance which we consider.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology