Expansion and Growth of Structure Observables in a Macroscopic Gravity
  Averaged Universe
  We investigate the effect of averaging inhomogeneities on expansion and
large-scale structure growth observables using the exact and covariant
framework of Macroscopic Gravity (MG). It is well-known that applying the
Einstein's equations and spatial averaging do not commute and lead to the
averaging problem. For the MG formalism applied to the
Friedmann-Lemaitre-Robertson-Walker (FLRW) metric, this gives an extra
dynamical term encapsulated as an averaging density parameter denoted
$\Omega_A$. An exact isotropic cosmological solution of MG for the flat FLRW
metric is already known in the literature, we derive here an anisotropic exact
solution. Using the isotropic solution, we compare the expansion history to
current data of distances to supernovae, Baryon Acoustic Oscillations, CMB last
scattering surface, and Hubble constant measurements, and find $-0.05 \le
\Omega_A \le 0.07$ (at the 95% CL). For the flat metric case this reduces to
$-0.03 \le \Omega_A \le 0.05$. We also find that the inclusion of this term in
the fits can shift the values of the usual cosmological parameters by a few to
several percents. Next, we derive an equation for the growth rate of large
scale structure in MG that includes a term due to the averaging and compare it
to that of the LCDM concordance model. We find that an $\Omega_A$ of an
amplitude range within the bounds above leads to a relative deviation of the
growth from that of the LCDM of up to 2-4% at late times. Thus, the shift in
the growth could be of comparable amplitude to that caused by similar changes
in cosmological parameters like the dark energy density parameter or its
equation of state. The effect could also be comparable in amplitude to some
systematic effects considered for future surveys. This indicates that the
averaging term and its possible effect need to be tightly constrained in future
precision cosmological studies. (Abridged)
