Two-branes with variable tension model and the effective Newtonian constant

It is shown that, in the two brane time variation model framework, if the hidden brane tension varies according to the phenomenological Eötvös law, the visible brane tension behavior is such that its time derivative is negative in the past and positive after a specific time of cosmological evolution. This behavior is interpreted in terms of a useful mechanical system analog and its relation with the variation of the Newtonian (effective) gravitational “constant” is explored.