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arXiv · 2201.01957

Gravitational energy-momentum pseudo-tensor in Palatini and metric $f(R)$ gravity

H. Abedi·S. Capozziello·M. Capriolo·A. M. Abbassi
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Abstract

We derive the gravitational energy-momentum pseudo-tensor $τ^μ_{\phantomμν}$ in both Palatini and metric approaches to $f(R)$ gravity. We then obtain the related cosmological gravitational energy density. Considering a flat Friedmann-Lemaître-Robertson-Walker spacetime, the energy density complex of matter and gravitation vanishes in the metric approach, but results non-vanishing in the Palatini formalism. This feature could be relevant in order to physically discriminate between the two approaches.

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H. Abedi, S. Capozziello, M. Capriolo, A. M. Abbassi. 2022-01-06. Gravitational energy-momentum pseudo-tensor in Palatini and metric $f(R)$ gravity. https://doi.org/10.1016/j.aop.2022.168796

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