Weakly Inhomogeneous models for the Low-Redshift Universe

Abstract: We analyze two different algorithms for constructing weakly inhomogeneous models for the low-redshift Universe, in order to provide a tool for testing the geodesic dynamics, within the sphere of validity for the Universe acceleration. We first implement the so-called quasi-isotropic solution in the late Universe, when a pure dark energy equation of state for the cosmological perfect fluid is considered. We demonstrate, that a solution exists only if the physical scale of the inhomogeneities is larger then the Hubble scale of the microphysics, which implies that inhomogeneities could not be observed at present-stage time. Then, we analyze a weakly deformed isotropic Universe toward a spherically symmetric model, thought as the natural metric framework of the {\Lambda}CDM model. We find that inhomogeneities will arise in the previous context as small perturbations of the order of few point percent over the background FRW universe. The obtained picture offers a useful scenario to investigate the influence of the inhomogeneity spectrum (left free in the obtained solution), on the propagation of photons or gravitational waves at low redshift values, and in line of principle may be used to account for several present-stage cosmological problems, such as the Hubble Tension.