Noether gauge symmetry for f(R) gravity in Palatini formalism

Abstract

In this study, we consider a flat FriedmannRobertson-Walker (FRW) universe in the context of Palatini f (R) theory of gravity. Using the dynamical equivalence between f (R) gravity and scalar-tensor theories, we construct a point Lagrangian in the flat FRW spacetime. Applying Noether gauge symmetry approach for this f (R) Lagrangian we find out the form of f (R) and the exact solution for cosmic scale factor. It is shown that the resulting form of f (R) yield a powerlaw expansion for the scale factor of the universe.

Anisotropic solution in phantom cosmology via Noether symmetry approach

“…This approach has been studied for many extended theories in cosmology [14,19,21,[28][29][30][31][32][33][34][35]. The Noether theorem states that if the Lie derivative of a given Lagrangian L, dragging along a vector field X vanishes…”

Scalar tensor teleparallel dark gravity via Noether symmetry

“…We also note that the Noether symmetry approach allows one to choose the potential dynamically in the scalar-tensor gravity theory [56][57][58][59][60][61][62][63][64], and the explicit form of the function f (R) of the modified f (R) theories of gravity [65][66][67][68][69][70][71]. In this form of f (R), cosmological solutions in the case of FRW metric can describe the accelerated period of the Universe.…”

The geometric nature of approximate Noether gauge symmetries

“…The Noether gauge symmetry (NGS) approach [5][6][7][8][9][10][11] is a generalization of the strict Noether symmetry approach [12][13][14] in the sense that Noether symmetry equation includes a gauge term in such a way that the vector field X = ξ∂ s +η a ∂ ∂ x a is called a NGS of a Lagrangian L if there exists a gauge function, A(s, x a ), such that the Noether symmetry condition holds [3,4] X…”