A note on covariant conservation of energy–momentum in modified gravities

By Tomi Koivisto. 2005

215 citations recorded by the source corpus.

An explicit proof of the vanishing of the covariant divergence of the energy–momentum tensor in modified theories of gravity is presented. The gravitational action is written in arbitrary dimensions and allowed to depend nonlinearly on the curvature scalar and its couplings with a scalar field. Also the case of a function of the curvature scalar multiplying a matter Lagrangian is considered. The proof is given both in the metric and in the first-order formalism, i.e. under the Palatini variational principle. It is found that the covariant conservation of energy–momentum is built in to the field equations. This crucial result, called the generalized Bianchi identity, can also be deduced directly from the covariance of the extended gravitational action. Furthermore, in all of these cases, the freely falling world lines are determined by the field equations alone and turn out to be the geodesics associated with the metric compatible connection. The independent connection in the Palatini formulation of these generalized theories does not have a similar direct physical interpretation. However, in the conformal Einstein frame a certain bi-metricity emerges into the structure of these theories.

View Paper: https://www.semanticscholar.org/paper/f1518fdfd9545a4dd289033a28e3eda62fa5a54b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Generalized Curvature-Matter Couplings in Modified Gravity (2014, methodology): “Taking into account the covariant divergence of Equation (134), with the use of the following mathematical identity [50]:”
f(R) Theories (2010, background): “In this section we study the evolution of matter density perturbations to confront Palatini f (R) gravity with the observations of large-scale structure [359, 356, 357, 598, 380, 597].”
Accelerating Cosmologies with an Anisotropic Equation of State (2007, unknown): “One may check that the sum ρφ + pφ satisfies the consistency relation ρφ + pφ = −ρ̇φ/(3H), which follows from the covariant conservation of matter that applies now since the Lm is minimally coupled [79].”
Nonmetricity formulation of general relativity and its scalar-tensor extension (2018, background): “[43] Tomi Koivisto, “Covariant conservation of energy momentum in modified gravities,” Class.”