f ( R )-gravity from Killing tensors

Abstract

We consider f (R)-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of f (R) and the field equations to be invariant under Lie-Bäcklund transformations which are linear in the momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether's Theorem. We find three new integrable f (R) models, for which with the application of the conservation laws we reduce the field equations to a system of two firstorder ordinary differential equations. For each model we study the evolution of the cosmological fluid. Where we find that for the one integrable model the cosmological fluid has an equation of state parameter, in which in the latter there is a linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder (CPL) parametric dark energy model. 95.35.+d, 95.36.+x

Cosmological evolution and exact solutions in a fourth-order theory of gravity

“…The reason that this is possible is that the Lagrangian of the field equations admits a Noetherian conservation law which is not generated by point symmetries as in the potential V 1 (φ) but from generalized symmetries. In particular the Killing tensor of the minisuperspace provides a contact symmetry (see [61] and references therein).…”

Fermion localization in higher curvature and scalar–tensor theories of gravity

“…Moreover, the overall normalization constants in Eqs. (38) and (39) are determined by using the normalization condition presented earlier in Eq. (35).…”

“…Such terms also have their origin in string theory from quantum corrections. In this context F(R) [32][33][34][35][36][37][38], GaussBonnet (GB) [39][40][41] or more generally Lanczos-Lovelock gravity are some of the candidates in higher curvature gravitational theory.…”

Radion stabilization in higher curvature warped spacetime

“…Such terms also have their origin in String theory due to quantum corrections. F(R) [31][32][33], Gauss-Bonnet (GB) [34][35][36] or more generally Lanczos-Lovelock gravity are some of the candidates in higher curvature gravitational theory.…”