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

Abstract

We derive the gravitational energy-momentum pseudo-tensor ${\tau }_{\nu }^{\mu }$ 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.

arXiv comment9 pages

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Cited by in corpus (4)

• Gravitational tensor and scalar modes in $f(Q,B)$ non-metric gravity
• The energy-momentum complex in non-local gravity
• Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity
• The gravitational energy-momentum pseudo-tensor in $f(Q)$ non-metric gravity