Mimicking Dark Energy with the backreactions of gigaparsec inhomogeneities

Spatial averaging and time evolving are non-commutative operations in General Relativity, which questions the reliability of the FLRW model. The long standing issue of the importance of backreactions induced by cosmic inhomogeneities is addressed for a toy model assuming a peak in the primordial spectrum of density perturbations and a simple CDM cosmology. The backreactions of initial Hubble-size inhomogeneities are determined in a fully relativistic framework, from a series of simulations using the BSSN formalism of numerical relativity. In the FLRW picture, these backreactions can be effectively described by two so-called morphon scalar fields, one of them acting at late time like a tiny cosmological constant. Initial density contrasts ranging from $10^{-2}$ down to $10^{-4}$, on scales crossing the Hubble radius between $z\sim 45 $ and $z\sim 1000$ respectively, i.e. comoving gigaparsec scales, mimic a Dark Energy (DE) component that can reach $\Omega_{\mathrm{DE}} \approx 0.7$ when extrapolated until today. A similar effect is not excluded for lower density contrasts but our results are then strongly contaminated by numerical noise and thus hardly reliable. A potentially detectable signature of this scenario is a phantom-like equation of state $w< -1$, at redshifts $z\gtrsim 4$ for a density contrast of $10^{-2}$ initially, relaxing slowly to $w \approx -1$ today. This new class of scenarios would send the fine-tuning and coincidence issues of Dark energy back to the mechanism at the origin of the primordial power spectrum enhancement, possibly in the context of inflation.