  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.
