We develop a novel model for Cosmological Hyperfluids, that is fluids with intrinsic hypermomentum that induce spacetime torsion and non-metricity. Imposing the Cosmological Principle to Metric-Affine Spaces, we present the most general covariant form of the hypermomentum tensor in an FLRW Universe along with its conservation laws and therefore construct a novel hyperfluid model for Cosmological purposes... Extending the previous model of the unconstrained hyperfluid in a Cosmological setting we establish the conservation laws for energy-momentum and hypermomentum and therefore provide the complete Cosmological setup to study non-Riemannian effects in Cosmology. With the help of this we find the forms of torsion and non-metricity that were earlier reported in the literature and also obtain the most general form of the Friedmann equations with torsion and non-metricity. We also discuss some applications of our model, make contact with the known results in the literature and point to future directions. (read more)