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Non perturbative effects of primordial curvature perturbations on the apparent value of a cosmological constant

We study effects on the luminosity distance of a local inhomogeneity seeded by primordial curvature perturbations of the type predicted by the inflationary scenario and constrained by the cosmic microwave background radiation. We find that a local underdensity originated from a one, two or three standard deviations peaks of the primordial curvature perturbations field can induce corrections to the value of a cosmological constant of the order of $0.6%,1%,1.5%$ respectively. These effects cannot be neglected in the precision cosmology era in which we are entering. Our results can be considered an upper bound for the effect of the monopole component of the local non linear structure which can arise from primordial curvature perturbations and requires a fully non perturbative relativistic treatment.