Gravitational energy–momentum pseudo-tensor in Palatini and metric [formula omitted] gravity

Abstract

We derive the gravitational energy–momentum pseudo-tensor τμνμ 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.