Multiscale cosmology and structure-emerging Dark Energy: A plausibility analysis

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 $\lambda_{\CM}$ 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 $\lambda_{\CM_{0}}$, the matter density $\Omega_{m}^{\CD_{0}}$, and the Hubble rate $H_{\CD_{0}}$ of today's Universe. Taking standard values for $\Omega_{m}^{\CD_{0}}$ and $H_{\CD_{0}}$ as well as a reasonable value for $\lambda_{\CM_{0}}$, 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 $\Lambda$CDM--like behavior of the scale factor, parametrized by the same parameters $\Omega_{m}^{\CD_{0}}$ and $H_{\CD_{0}}$, but without a cosmological constant. However, the temporal behavior of $\lambda_{\CM}$ does not faithfully reproduce the structure formation history. Surprisingly, however, the model matches with structure formation with the assumption of a low matter content, $\Omega_{m}^{\CD_{0}}\approx3\%$, a result that hints to a different interpretation of part of the backreaction effect as kinematical Dark Matter. (truncated)