  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.
