\right] > 0$$ give $$\label{rest1}
\sigma > 0 \, , \quad \sigma > \frac{\Lambda_{\rm b}m^2}2 \, , \quad
\Lambda_{\rm RS} \equiv \frac{\Lambda_{\rm b}}2 + \frac{\sigma^2}{3 M^6} > 0 \,
.$$

[**BRANE2:**]{} The inequalities $$C_1 \equiv \frac{\sigma}{3m^2} + \frac2{\ell^2} \left[ 1 + \sqrt{1+\ell^2
\left(\frac{\sigma}{3m^2} - \frac{\Lambda_{\rm b}}{6}\right)} \right] > 0$$ and $$C_2 \equiv \frac{1}{3m^2} \left[ 1 + \frac{1}{\sqrt{1+\ell^2 \left(
\frac{\sigma}{3m^2} - \frac{\Lambda_{\rm b}}{6} \right)}} \right] > 0$$ imply $$\label{rest2}
\sigma > -\frac{6m^2}{\ell^2}\, , \quad \sigma > \frac{\Lambda_{\rm b} m^2}2 -
\frac{3m^2}{\ell^2}\, .$$

From these relations, one can see that BRANE2 model with the asymptotic conditions (\[low-energy\]), in principle, can have negative brane tension, while the tension of the BRANE1 model is restricted to be positive.

The physical restrictions formulated above are necessary for a reasonable braneworld theory with the asymptotic limit (\[low-energy\]) reached today, but they are certainly far from being sufficient for the consistency of a braneworld model with all cosmological observations (cosmic microwave background, big-bang nucleosynthesis, etc). This important issue, which, in fact, constitutes the main subject of investigations in the braneworld theory, clearly lies beyond the scope of the present paper and will be considered in our future publications. At the moment, one can only note that the 