Cosmic Inhomogeneities and Averaged Cosmological Dynamics

If general relativity (GR) describes the expansion of the Universe, the observed cosmic acceleration implies the existence of a “dark energy.” However, while the Universe is on average homogeneous on large scales, it is inhomogeneous on smaller scales. While GR governs the dynamics of the inhomogeneous Universe, the averaged homogeneous Universe obeys modified Einstein equations. Can such modifications alone explain the acceleration? For a simple generic model with realistic initial conditions, we show the answer to be “no.” Averaging effects negligibly influence the cosmological dynamics.

Figure 1

The evolution of $-{\mathcal{S}}^{(1)}/6H^2$. Also shown is a hypothetical curvaturelike correction, evolving like $\sim a^{-2}$.

Figure 2

The normalized evolution of the backreaction functions other than ${\mathcal{S}}^{(1)}$. To enhance contrast, a strongly decaying early time mode for ${\mathcal{P}}^{(1)}/H^2$ has not been shown.