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.

9 pages

References in corpus (6)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Palatini Approach to Modified Gravity: f(R) Theories and Beyond
• Bouncing Cosmologies in Palatini $f(R)$ Gravity
• Power-law cosmic expansion in f(R) gravity models
• Energy-momentum complexes in f(R) theories of gravity
• Cosmological perturbations in gravitational energy-momentum complex

Cited by in corpus (1)

• Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity