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 and backreaction terms. For the MG formalism applied to the Friedman-Lemaitre-Robertson-Walker (FLRW) metric, the extra term can be encapsulated as an averaging density parameter denoted ${\mathrm{\Omega }}_{\mathcal{A}}$. 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 available data of distances to supernovae, baryon acoustic oscillations, cosmic microwave background last scattering surface data, and Hubble constant measurements, and find $-0.05\le {\mathrm{\Omega }}_{\mathcal{A}}\le 0.07$ (at the 95% confidence level). For the flat metric case this reduces to $-0.03\le {\mathrm{\Omega }}_{\mathcal{A}}\le 0.05$. The positive part of the intervals can be rejected if a mathematical (and physical) prior is taken into account. 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 assess its effect on the evolution of the growth compared to that of the Lambda cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) concordance model. We find that an ${\mathrm{\Omega }}_{\mathcal{A}}$ term of an amplitude range of [$-0.04,-0.02$] lead to a relative deviation of the growth from that of the $\mathrm{\Lambda }\mathrm{CDM}$ 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.

• Received 26 December 2014

DOI:https://doi.org/10.1103/PhysRevD.91.063534