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We use anisotropic fluid cosmology to describe the present, dark energy-dominated, universe. Similarly to what has been proposed for galactic dynamics, the anisotropic fluid gives an effective description of baryonic matter, dark energy and their possible interaction, without assuming the presence of dark matter. The resulting anisotropic fluid spacetime naturally generates inhomogeneities at small scales, triggered by an anisotropic stress, and could therefore be responsible for structure formation at these scales. Solving the cosmological equations, we show that the dynamics of the scale factor $a$ is described by usual FLRW cosmology and decouples completely from that describing inhomogeneities. We assume that the cosmological anisotropic fluid inherits the equation of state from that used to describe galaxy rotation curves. We show that, in the large scale regime, the fluid can be described as a generalized Chaplygin gas and fits well the distance modulus experimental data of type Ia supernovae, thus correctly modelling the observed accelerated expansion of the universe. Conversely, in the small scale regime, we use cosmological perturbation theory to derive the power spectrum $P(k)$ for mass density distribution. At short wavelengths, we find a $1/k^4$ behaviour, in good accordance with the observed correlation function for matter distribution at small scales.