The high value of brane tension has a crucial role in recovering Einsteins general relativity at low energies. In the framework of a recently developed formalism with variable brane tension one can pose the question, whether it was always that high? In analogy with fluid membranes, in this paper we allow for temperature dependent brane tension, according to the corresponding law established by Eotvos. For cosmological branes this assumption leads to several immediate consequences: (a) The brane Universe was created at a finite temperature $T_{c}$ and scale factor $a_{min}$. (b) Both the brane tension and the 4-dimensional gravitational coupling constant increase with the scale factor from zero to asymptotic values. (c) The 4-dimensional cosmological constant evolves with $a$, starting with a huge negative value, passing through zero, finally reaching a small positive value. Such a scale-factor dependent cosmological constant is able to generate a surplus of attraction at small $a$ (as dark matter does) and a late-time repulsion at large $a$ (dark energy). In the particular toy model discussed here the evolution of the brane tension is compensated by energy interchange between the brane and the fifth dimension, such that the continuity equation holds for the cosmological fluid. The resulting cosmology closely mimics the standard model at late times, a decelerated phase being followed by an accelerated expansion. The energy absorption of the brane drives the 5D space-time towards maximal symmetry, becoming Anti de Sitter.
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