Notes on the two-brane model with variable tension

Motivated by possible extensions of the braneworld models with two branes, we investigate some consequences of a variable brane tension, using the well established results on consistency conditions. By a slight modification of the usual stress-tensor used in order to derive the braneworld sum rules, we find some important constraints obeyed by time-dependent brane tensions. In particular, it is shown that the tensions of two Randall-Sundrum\char21{}like branes obeying, at the same time, an E\"otv\"os law, aggravate the fine-tuning problem. Also, it is shown that if the hidden brane tension obeys an E\"otv\"os law, then the visible brane has a mixed behavior allowing a bouncinglike period at early times while it is dominated by an E\"otv\"os law now. To finalize, we discuss some qualitative characteristics, which may arise in the scope of dynamical brane tensions, as anisotropic background and branons production.