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We consider a generic Metric-Affine Cosmological setup and classify someparticularly interesting specific cases of Perfect Hyperfluids. In particular,we present the form of conservation laws for the cases of pure spin, puredilation and pure shear fluids. We also develop the concept of anincompressible hyperfluid and pay special attention to the case of ahypermomentum preserving hyperfluid. We also give a specific example on theemergence of the spin, dilation and shear currents through matter-connectioncouplings. In addition, starting from the generalized acceleration equation forthe scale factor including torsion and non-metricity we provide a firstintegral of motion relating the latter with the rest of the hyperfluidvariables. These results then formalize the analysis of the non-Riemannianeffects in Cosmology.

Metric-Affine Cosmologies: Kinematics of Perfect (Ideal) Cosmological Hyperfluids and First Integrals