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

Abstract

We derive the gravitational energy-momentum pseudo-tensor tau(mu)(upsilon) in both Palatini and metric approaches to f (R) gravity. We then obtain the related cosmological gravitational energy density. Considering a flat Friedmann-Lemaitre-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.