values of the constants $C_1$ and $C_2$ in a braneworld that today evolves in regime (\[low-energy\]) are roughly constrained by the values of the detected cosmological constant and gravitational coupling, respectively, as $$C_1 \simeq 0.7 H_0^2 \, , \qquad C_2 \simeq \frac{8 \pi G_{\rm N}}{3} \, ,$$ where $H_0 \approx 73\, {\rm km/sec} \cdot {\rm Mpc}$ is the current value of the Hubble parameter, and $G_{\rm N}$ is Newton’s constant. With these constraints, there remains a considerable freedom in the parameter space of the theory, which is to be further restricted by a more careful analysis.

If condition (\[regime\]) is not satisfied today, then regime (\[low-energy\]) has not yet been reached, and one should turn to the general evolution equation (\[first\]), which has a rather rich and interesting phenomenology for modeling dark energy [@SS; @AS]. For example, the current acceleration of the universe expansion may be described by a braneworld model which has $C_1 = 0$ in the asymptotic expansion (\[low-energy\]). According to this model, the current acceleration of the cosmological expansion is temporary, and the future evolution proceeds in a matter-dominated regime (see [@SS] for more details). Another interesting example is the model of loitering braneworld [@loiter], which can 