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 .