# Averaging in Cosmology

Although the universe is homogeneous and isotropic at large cosmological scales, density perturbations can be very large at small scales (e.g., galaxies, stars, etc.). When passing from the small scale description, where Einstein’s equation holds, to the large scale description, some sort of averaging is necessary. This is nontrivial because the Einstein equation is nonlinear, so that small scale structure can potentially affect the large scale dynamics. In other words, even if the averaged universe has FLRW symmetry, it is not clear that the Friedman equation holds. It has even been suggested that such effects could mimic a cosmological constant.

R. Wald and I developed a framework in which such “backreaction” effects could be calculated, and proved that the only way in which significant effects could occur is via gravitational radiation, thus ruling this scenario out as an explanation for Dark Energy. We then used this framework to establish a perturbative relationship between Newtonian and relativistic cosmology.