Cosmic structure, averaging and dark energy
  These lecture notes review the theoretical problems associated with
coarse-graining the observed inhomogeneous structure of the universe at late
epochs, of describing average cosmic evolution in the presence of growing
inhomogeneity, and of relating average quantities to physical observables. In
particular, a detailed discussion of the timescape scenario is presented. In
this scenario, dark energy is realized as a misidentification of gravitational
energy gradients which result from gradients in the kinetic energy of expansion
of space, in the presence of density and spatial curvature gradients that grow
large with the growth of structure. The phenomenology and observational tests
of the timescape model are discussed in detail, with updated constraints from
Planck satellite data. In addition, recent results on the variation of the
Hubble expansion on < 100/h Mpc scales are discussed. The spherically averaged
Hubble law is significantly more uniform in the rest frame of the Local Group
of galaxies than in the conventional rest frame assumed for the Cosmic
Microwave Background. This unexpected result supports a fundamental revision of
the notion of the cosmic rest frame, consistent with the expectations of the
timescape scenario.
