Novel Approach to Cosmological Nonlinearities as an Effective Fluid

We propose a two parameters extension of the flat ΛCDM model to capture the impact of matter inhomogeneities on our cosmological inference. Non virialized but nonlinearly evolving overdense and underdense regions, whose abundance is quantified using the Press-Schechter formalism, are collectively described by two effective perfect fluids ρ_{c}, ρ_{v} with nonvanishing equation of state parameters w_{c,v}≠0. These fluids are coupled to the pressureless dust, akin to an interacting DM-DE scenario. The resulting phenomenology is very rich, and could potentially address a number of inconsistencies of the standard model, including a simultaneous resolution of the Hubble and σ_{8} tensions. To assess the viability of the model, we set initial conditions compatible to the Planck 2018 best fit ΛCDM cosmology and fit its additional parameters using SN Ia observations from DESY5, BAO distances from DESI DR2 and a sample of uncorrelated fσ_{8} measurements. Our findings show that backreaction effects from the cosmic web could restore the concordance between early and late Universe cosmological probes.