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Spatial averaging and time evolving are non-commutative operations in GeneralRelativity, which questions the reliability of the FLRW model. The longstanding issue of the importance of backreactions induced by cosmicinhomogeneities is addressed for a toy model assuming a peak in the primordialspectrum of density perturbations and a simple CDM cosmology. The backreactionsof initial Hubble-size inhomogeneities are determined in a fully relativisticframework, from a series of simulations using the BSSN formalism of numericalrelativity. In the FLRW picture, these backreactions can be effectivelydescribed by two so-called morphon scalar fields, one of them acting at latetime 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 $\Omega_{\mathrm{DE}} \approx0.7$ when extrapolated until today. A similar effect is not excluded for lowerdensity contrasts but our results are then strongly contaminated by numericalnoise and thus hardly reliable. A potentially detectable signature of thisscenario 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 andcoincidence issues of Dark energy back to the mechanism at the origin of theprimordial power spectrum enhancement, possibly in the context of inflation.

Mimicking Dark Energy with the backreactions of gigaparsec inhomogeneities