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

Abstract

Using the exact Lemaitre-Bondi-Tolman solution with a non-vanishing cosmological constant Λ, 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 spacetime 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 ΛCDM 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 Λ.2

Low-redshift effects of local structure on the Hubble parameter in presence of a cosmological constant

“…Now we can find the low redshift Taylor expansion for the geodesic equations [19], and then we calculate the Hubble parameter. We expand the solution of the geodesic equations according to…”

“…The effects of a local inhomogeneity on cosmological observations have been studied already for different cases [1, such as the equation of state of dark energy or the luminosity distance [18,19,23]. It has been shown for example that the value of the cosmological constant could be affected significantly by the presence of local inhomogeneity seeded by primordial curvature perturbations [9], which could also lead to the wrong conclusion of a varying equation of state for dark energy while only a cosmological constant is present [19].…”

“…It has been shown for example that the value of the cosmological constant could be affected significantly by the presence of local inhomogeneity seeded by primordial curvature perturbations [9], which could also lead to the wrong conclusion of a varying equation of state for dark energy while only a cosmological constant is present [19]. The origin of these effects is that spatial inhomogeneities can change the energy of the propagating photons, contaminating the cosmological redshift due to the Universe expansion and consequently introducing some errors in the estimation of parameters based on cosmological models which ignore the effects of the inhomogeneities.…”

Low-redshift formula for the luminosity distance in a LTB model with cosmological constant

“…As a consequence the formulas we obtain only depend on K i , and they do not require any addition calculation. We now find a local Taylor expansion in redshift for the geodesics equations [9], and we then calculate the luminosity distance. The general expression is rather cumbersome, and is given in the appendix.…”

“…One of the main assumptions of the standard cosmological model used in fitting these observational data is spatial homogeneity of the Universe. We cannot nevertheless exclude the presence of a local inhomogeneity around us which could affect our interpretation of the cosmological data [9][10][11].…”