Validity conditions for linear cosmological perturbations

Full text: One of the main issues concerning back-reaction in cosmology is to validate the use of linear order perturbation to evolve the large-scale metric despite the presence of structure formation. After the appearance of cosmic structure such as galaxies, cluster and voids, the local dynamics becomes extremely non-linear and the local mass density can become 30 order of magnitude higher than the average mass density of the universe. Thus, it is certain that the matter evolution in small-scales is far from linear. Notwithstanding, at the same time the large scale metric perturbations are still perturbatively small. The LCDM model and the need for dark energy rest in the fact that the departure from FLRW metric is small and the linearized Einstein equations are the correct system to evolve them. However, it is still an open question whether or not the small-scale clumpiness can affect the evolution of the large-scales. We shall consider the validity conditions that could support the use of a homogeneous and isotropic metric to describe the universe in the large and show that the arguments found in the literature generally do not justify its applicability. We also stress that our treatment is covariant and gauge independent which allow to immediately compare with different approaches such as the 3+1 covariant approach first introduced by Hawking, Ehlers and Ellis. (author)