Lightcone Averaging and Precision Cosmology
  The first objective of this thesis is to fill the lack in cosmology of a
description on the past light cone: the null hypersurface on which observed
signals propagate. Its second goal is to evaluate the importance of
inhomogeneities in the determination of dark energy parameters, whose real
nature is still unknown and for which the influence of matter structures has
been proposed as a cosmological alternative. We start with the definition of a
"geodesic lightcone" gauge simplifying greatly the study of light propagation
in the Universe. We then define a gauge invariant average of scalars on the
past light cone and compute the effect of inhomogeneities on the luminosity
flux by considering their power spectrum up to its non-linear regime. The
effect on the flux is negligible whereas observables like the luminosity
distance, computed at second order in perturbations, are much more affected. We
also study the distance modulus at the basis of the discovery of dark energy
from type Ia supernovae (SNe). The average of this modulus is only slightly
affected by inhomogeneities but its variance sensitively depends on them. These
results show, within their hypotheses, that an alternative to dark energy by an
effect of structures is impossible but, at the same time, emphasize their
importance on the dispersion of data in the Hubble diagram. The dominating
physical effects turn out to be peculiar velocity of SNe and weak lensing. Our
predictions on the dispersion are in very good agreement with first analyses
carried out so far to detect a signal of lensing among SNe Ia data and will be
testable in the near future.
