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

We derive the gravitational energy–momentum pseudo-tensor τ μ ν μ 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. • Gravitational energy–momentum pseudotensor. • Palatini f(R) gravity. • Metric f (R) gravity. • Cosmological background. [ABSTRACT FROM AUTHOR]