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arXiv · 2104.10192

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

Damianos Iosifidis
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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.

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Damianos Iosifidis. 2021-04-20. Riemann Tensor and Gauss-Bonnet density in Metric-Affine Cosmology. https://doi.org/10.1088/1361-6382%2Fac213a

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