Is backreaction really small within concordance cosmology?
  Smoothing over structures in general relativity leads to a renormalisation of
the background, and potentially many other effects which are poorly understood.
Observables such as the distance-redshift relation when averaged on the sky do
not necessarily yield the same smooth model which arises when performing
spatial averages. These issues are thought to be of technical interest only in
the standard model of cosmology, giving only tiny corrections. However, when we
try to calculate observable quantities such as the all-sky average of the
distance-redshift relation, we find that perturbation theory delivers divergent
answers in the UV and corrections to the background of order unity. There are
further problems. Second-order perturbations are the same size as first-order,
and fourth-order at least the same as second, and possibly much larger, owing
to the divergences. Much hinges on a coincidental balance of 2 numbers: the
primordial power, and the ratio between the comoving Hubble scales at
matter-radiation equality and today. Consequently, it is far from obvious that
backreaction is irrelevant even in the concordance model, however natural it
intuitively seems.
