Riemann Tensor and Gauss-Bonnet density in Metric-Affine Cosmology

Abstract

We analytically derive the covariant form of the Riemann (curvature) tensor for homogeneous Metric-Affine Cosmologies. That is, we present, in a Cosmological setting, the most general covariant form of the full Riemann tensor including also its non-Riemannian pieces which are associated to spacetime torsion and non-metricity. Having done so we also compute a list of the curvature tensor by-products such as Ricci tensor, homothetic curvature, Ricci scalar, Einstein tensor etc. Finally we derive the generalized Metric-Affine version of the usual Gauss-Bonnet density in this background and demonstrate how under certain circumstances the latter represents a total derivative term.

15 pages, no figures

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Cited by in corpus (7)

• Cosmology of Quadratic Metric-Affine Gravity
• FLRW Cosmology in Metric-Affine $F(R,Q)$ Gravity
• Myrzakulov $F(T,Q)$ gravity: cosmological implications and constraints
• (3+1)-Formulation for Gravity with Torsion and Non-Metricity II: The Hypermomentum Equation
• Cosmology of Metric-Affine $R+\beta R^2$ Gravity with Pure Shear Hypermomentum
• Metric-Affine Version of Myrzakulov $F(R,T,Q,\mathcal{T})$ Gravity and Cosmological Applications
• Inflation with the Gauss-Bonnet term in the Palatini formulation