  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.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology