Dynamical heredity from f(R)-bulk to braneworld: Curvature dynamical constraint and f(R)-unimodular gravity

Abstract

Recently, Borzou et al. (BSSY) generalized the Shiromizu–Maeda–Sasaki (SMS) formulation to [Formula: see text]-bulks. BSSY brane projected equation carries an additional stress tensor, besides SMS correction for Einstein’s theory on the brane. If we change this perspective, by requiring BSSY tensor in the geometrical side, acting as [Formula: see text]-brane generator, it is possible to relate [Formula: see text]-brane/bulk theories, by using curvature dynamical constraint (CDC), a concept that we developed. Since brane and bulk are [Formula: see text], 5D/4D scalar curvatures also play a dynamical role and, thus, a dynamical version to Gauss equation trace, or CDC, must be offered. We will work yet in a specific case to obtain [Formula: see text]-unimodular gravity, formally identical with that obtained by Nojiri et al. (NOO). Therefore, two applications which consider cosmological scenarios in [Formula: see text]-unimodular gravity with dark radiation correction will be offered.