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

Abstract

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 by varying the action with respect to the metric and the independent connection. Subsequently, considering a Friedmann-Lemaître-Robertson-Walker background, we derive the modified Friedmann equations in the presence of a perfect cosmological hyperfluid. Especially, we focus on the particular case in which $f(R)=R+\beta R^2$, considering purely shear hypermomentum and finding exact solutions in the weak coupling limit.

26 pages

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• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
• General Einstein-Cartan quadratic gravity with derivative couplings
• Algebraic classification of the gravitational field in general metric-affine geometries
• Inflationary assessment of $F(\mathcal{R},\tilde{\mathcal{R}})$ Einstein-Cartan models