Highly homogeneous and isotropic universes: quasi-dust models and the apparent dark-energy evolution arising from the local gravitational potential

Abstract

In this manuscript, we develop a class of inhomogeneous relativistic cosmological models with the following properties: (i) They contain cosmological observers to whom the spatial geometry and the expansion are homogeneous and isotropic; (ii) Matter behaves closely to dust, as it is formed by an ensemble of massive particles whose number density $4$-vector is conserved and reacts viscously to the local tidal forces; (iii) They generalize the dust FLRW model; (iv) They give rise to effective models on large scales that reproduce the FLRW behaviour with dust and a running dark-energy term, which appears as a backreaction effect from the local gravitational potential; (v) By suitably setting the distribution of energy in the current universe, the effective large-scale equation-of-state parameter can reproduce, in principle, any polynomial on the scale factor whose term of order zero is negative; (vi) The luminous distance observations imply an apparent large-scale acceleration, as the deceleration parameter is negative, while in reality the universe is decelerating.