Testing scale-dependent perturbations in ΛCDM with future galaxy surveys

Abstract

Abstract The quest for the origin of the present accelerated expansion of the Universe is still open. By means of the present geometrical and dynamical observational data, it is very hard to establish, from a statistical perspective, a clear preference among the vast majority of the proposed models for the dynamical dark energy and/or modified gravity theories alternative with respect to the standard Λ CDM scenario. On the other hand, on scales much smaller than present Hubble scale, there are possibly detectable differences in the growth of the matter perturbations for different modes of the perturbations, even in the context of the same Λ CDM model. In view of the new planned observations that will give insight into the perturbations of the dark sector, this issue is being worth of further investigation. Here, we analyze the evolution of the dark matter perturbations in the context of Λ CDM. We employ the scale-dependent perturbation equations for the growth function, and we abandon both the sub-Hubble approximation and the slowly varying potential assumption, which lead to the well known and most commonly used scale-independent solutions for the perturbations. We apply the Fisher Matrix approach to three future planned galaxy surveys e.g., DESI, Euclid, and WFirst-2.4, in order to have insights on the possibility to confute cosmological models through perturbations growth data in the next future. With the aforementioned surveys on hand, and only by dynamical probes, we will achieve multiple goals: 1 . the improvement in the accuracy of the determination of the f σ 8 will give the possibility to discriminate between Λ CDM and alternative dark energy models even in the scale-independent approach; 2 . it will be possible to test the goodness of the scale-independence finally, and also to quantify the necessity of a scale dependent approach to the growth of the perturbations, in particular using surveys which encompass redshift bins with scales k 0 . 005 h Mpc−1; 3 . the scale-dependence itself might add much more discriminating power in general, but further advanced surveys will be needed.