The Generalized f(R) Model with Coupling in 5D Spacetime

The generalized f(R) gravity with coupling in five-dimensional (5D) spacetime is studied on the basis of both the 4D generalized f(R) gravity with coupling and the pure f(R) gravity without coupling in 5D spacetime. Specifically, by assuming a hypersurface-orthogonal space-like Killing vector field in 5D spacetime, the generalization of the 4D generalized f(R) gravity to 5D can be realized, which can give the reduced 4-metric coupled with two scalar fields. In particular, we discuss a special class of models, i.e., f₁(R)=f₂(R)=αR^m (m≠1), and choose B(L_m)=L_m=?ρ in the homogeneous and isotropic cosmology with the 4D Friedmann–Robertson–Walker metric. The numerical analysis shows that the parameter m can be constrained by means of the current observations for the deceleration parameter, which implies that this generalized f(R) model with coupling in 5D spacetime can account for the present accelerated expansion of the universe.