Averaged universe confronted with cosmological observations: A fully covariant approach (1604.03503v2)

Abstract: 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.