Dark energy as a geometrical effect in geodetic brane gravity

Within the framework of the modified geodetic brane gravity, conformed by the Regge-Teitelboim model and enhanced with a linear term in the extrinsic curvature of the brane, the possibility that under an FRW geometry this theory emulates the so-called dark energy is discussed. The cosmological behavior of this model displays a self-(non-self)-accelerated expansion of this universe which is caused by a combination of usual matter and gravitational geometric effects controlled by a $\beta$ parameter that accompanies the correction $K$ term. Indeed, the self-accelerated branch, provided by the trace $K$ model raises the question of whether the extrinsic curvature correction terms might be suitable for dark energy candidates. We discuss the analytical expression obtained for $\rd$ in addition to the main cosmological parameters such as the state parameter $\omega_{\text{\tiny eff}}$ and the deceleration parameter $q$. Moreover, when we call for the contribution of dark radiation-like energy to be switched off, $\Odr \to 0$, we find the same acceleration behavior, as well as the same dark energy content provided by the DGP theory. The relationship of our findings to the analysis for $\rd$ performed by Davidson and Gurwich within the unified brane cosmology is briefly discussed.