Lessons fromf(R,Rc2,Rm2,Lm)gravity: Smoot

Abstract

Lessons from f (R, R Faculty of Science, Memorial University, St. John's, Newfoundland, Canada, A1C 5S7 Ivan Booth † Department of Mathematics and Statistics, Memorial University, St. John's, Newfoundland, Canada, A1C 5S7 This paper studies a generic fourth-order theory of gravity with Lagrangian density Gauss-Bonnet gravity with G denoting the Gauss-Bonnet invariant. We use Noether's conservation law to study the f (R 1 , R 2 . . . , R n , L m ) model with nonminimal coupling between L m and Riemannian invariants R i , and conjecture that the gradient of nonminimal gravitational coupling strength ∇ µ f L m is the only source for energy-momentum nonconservation.This conjecture is applied to the f (R, R Focusing on modifications of GR, the original Lagrangian density can be modified in two ways: (1) extending its dependence on the curvature invariants, and (2) In all these models, the spacetime geometry remains minimally coupled to the matter Lagrangian density L m .On the other hand, following the spirit of nonminimal f (R)L d coupling in scalar-field dark-energy models [9], for modified theories of gravity an extra term λf (R)L m was respectively added to the standard actions of GR and f (R) + 2κL m gravity in [10] and [11], which represents nonminimal curvature-matter coupling between R *

Generalized Curvature-Matter Couplings in Modified Gravity

“…In the minisuperspace spanned by the FRW scale factor and the Ricci scalar, the equivalence of the reduced action was examined, and the canonical quantization of the f (R, L m ) model was undertaken and the corresponding Wheeler-DeWitt equation derived. The introduction of the invariant contractions of the Ricci and Riemann tensors were further considered, and applications to black hole and wormhole physics were analyzed [104].…”

Lovelock–Brans–Dicke gravity

“…and the f R, , m ( ) L  [14] generalized Gauss-Bonnet gravities. Here we emphasize that the Gauss-Bonnet effects therein could all be simplified into the form of equation (33).…”

“…Einstein's equation supplemented by the cosmological constant Λ. These directions can allow for, for example, fourth and even higher order gravitational field equations [2][3][4][5], more than four spacetime dimensions [6,7], extensions of pure pseudo-Riemannian geometry and metric gravity [7,8], extra physical degrees of freedom [9][10][11][12], and nonminimal curvature-matter couplings [13,14]. From a variational approach, these violations manifest themselves as different modifications of the Hilbert-Einstein action, such as extra curvature invariants, scalar fields, and nonRiemannian geometric variables.…”