Effects of inhomogeneities on apparent cosmological observables: "fake" evolving dark energy

Using the exact Lemaitre-Bondi-Tolman solution with a non-vanishing cosmological constant $\Lambda$, we investigate how the presence of a local spherically-symmetric inhomogeneity can affect apparent cosmological observables, such as the deceleration parameter or the effective equation of state of dark energy (DE), derived from the luminosity distance under the assumption that the real space-time is exactly homogeneous and isotropic. The presence of a local underdensity is found to produce apparent phantom behavior of DE, while a locally overdense region leads to apparent quintessence behavior. We consider relatively small large scale inhomogeneities which today are not linear and could be seeded by primordial curvature perturbations compatible with CMB bounds. Our study shows how observations in an inhomogeneous $\Lambda$CDM universe with initial conditions compatible with the inflationary beginning, if interpreted under the wrong assumption of homogeneity, can lead to the wrong conclusion about the presence of "fake" evolving dark energy instead of $\Lambda$.