Averaged universe confronted with cosmological observations: A fully
  covariant approach
  One of the outstanding problems in general relativistic cosmology is that of
the averaging. That is, how the lumpy universe that we observe at small scales
averages out to a smooth Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The
root of the problem is that averaging does not commute with the Einstein
equations that govern the dynamics of the model. This leads to the well-know
question of backreaction in cosmology. In this work, we approach the problem
using the covariant framework of Macroscopic Gravity (MG). We use its
cosmological solution with a flat FLRW macroscopic background where the result
of averaging cosmic inhomogeneities has been encapsulated into a backreaction
density parameter denoted $\Omega_\mathcal{A}$. We constrain this averaged
universe using available cosmological data sets of expansion and growth
including, for the first time, a full CMB analysis from Planck temperature
anisotropy and polarization data, the supernovae data from Union 2.1, the
galaxy power spectrum from WiggleZ, the weak lensing tomography shear-shear
cross correlations from the CFHTLenS survey and the baryonic acoustic
oscillation data from 6Df, SDSS DR7 and BOSS DR9. We find that $-0.0155 \le
\Omega_\mathcal{A} \le 0$ (at the 68\% CL) thus providing a tight upper-bound
on the backreaction term. We also find that the term is strongly correlated
with cosmological parameters such $\Omega_\Lambda$, $\sigma_8$ and $H_0$. While
small, a backreaction density parameter of a few percent should be kept in
consideration along with other systematics for precision cosmology.
