  The canonical quantization of the modified geodetic brane cosmology which is
implemented from the Regge-Teitelboim model and the trace of the extrinsic
curvature of the brane trajectory, K, is developed. As a second-order
derivative model, on the grounds of the Ostrogradski Hamiltonian method and the
Dirac's scheme for constrained systems, we find suitable first- and
second-class constraints which allow for a proper quantization. We also find
that the first-class constraints obey a sort of truncated Virasoro algebra. The
effective quantum potential emerging in our approach is exhaustively studied
where it shows that an embryonic epoch is still present. The quantum nucleation
is sketched where we observe that it is driven by an effective cosmological
constant.
