Cosmological backreaction suggests a link between structure formation and the expansion history of the Universe. In order to quantitatively examine this connection, we dynamically investigate a volume partition of the Universe into over- and underdense regions. This allows us to trace structure formation using the volume fraction of the overdense regions ${\lambda }_{\mathcal{M}}$ as its characterizing parameter. Employing results from cosmological perturbation theory and extrapolating the leading mode into the nonlinear regime, we construct a three-parameter model for the effective cosmic expansion history, involving ${\lambda }_{{\mathcal{M}}_0}$, the matter density ${\Omega }_m^{{\mathcal{D}}_0}$, and the Hubble rate $H_{{\mathcal{D}}_0}$ of today’s Universe. Taking standard values for ${\Omega }_m^{{\mathcal{D}}_0}$ and $H_{{\mathcal{D}}_0}$ as well as a reasonable value for ${\lambda }_{{\mathcal{M}}_0}$, that we derive from $N$-body simulations, we determine the corresponding amounts of backreaction and spatial curvature. We find that the obtained values that are sufficient to generate today’s structure also lead to a $\Lambda \mathrm{CDM}$-like behavior of the scale factor, parametrized by the same parameters ${\Omega }_m^{{\mathcal{D}}_0}$ and $H_{{\mathcal{D}}_0}$, but without a cosmological constant. However, the temporal behavior of ${\lambda }_{\mathcal{M}}$ does not faithfully reproduce the structure formation history. Surprisingly, however, the model matches with structure formation with the assumption of a low matter content, ${\Omega }_m^{{\mathcal{D}}_0}\approx 3\%$, a result that hints to a different interpretation of part of the backreaction effect as kinematical dark matter. A complementary investigation assumes the $\Lambda \mathrm{CDM}$ fit-model for the evolution of the global scale factor by imposing a global replacement of the cosmological constant through backreaction, and also supposes that a Newtonian simulation of structure formation provides the correct volume partition into over- and underdense regions. From these assumptions we derive the corresponding evolution laws for backreaction and spatial curvature on the partitioned domains. We find the correct scaling limit predicted by perturbation theory, which allows us to rederive higher-order results from perturbation theory on the evolution laws for backreaction and curvature analytically. This strong backreaction scenario can explain structure formation and dark energy simultaneously. We conclude that these results represent a conceptually appealing approach towards a solution of the dark energy and coincidence problems. Open problems are the still too large amplitude of initial perturbations that are required for the scenarios proposed, and the role of dark matter that may be partially taken by backreaction effects. Both drawbacks point to the need of a reinterpretation of observational data in the new framework.

• Received 20 February 2010

DOI:https://doi.org/10.1103/PhysRevD.82.023523