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In this paper we study the cosmological aspects of metric-affine $f(R)$gravity with hyperfluid. The equations of motion of the theory are obtained byvarying the action with respect to the metric and the independent connection.Subsequently, considering a Friedmann-Lema\^itre-Robertson-Walker background,we derive the modified Friedmann equations in the presence of a perfectcosmological hyperfluid. Especially, we focus on the particular case in which$f(R)=R+\beta R^2$, considering purely shear hypermomentum and finding exactsolutions in the weak coupling limit.

Cosmology of Metric-Affine $R + \beta R^2$ Gravity with Pure Shear Hypermomentum