Slinky evolution of domain wall brane cosmology

Invoking an initial symmetry between the time $t$ and some extra spatial dimension $y$, we discuss a novel scenario where the dynamical formation of the 4-dim brane and its cosmological evolution are induced simultaneously by a common $t<->y$ symmetry breaking mechanism. The local maximum of the underlying scalar potential is mapped onto a 'watershed' curve in the $(t,y)$ plane; the direction tangent to this curve is identified as the cosmic time, whereas the perpendicular direction serves locally as the extra spatial dimension. Special attention is devoted to the so-called slinky configurations, whose brane cosmology is characterized by a decaying cosmological constant along the watershed curve. Such a slinky solution is first constructed within a simplified case where the watershed is constrained by $y = 0$. The physical requirements for a slinky configuration to generate a realistic model of cosmological evolution are then discussed in a more elaborated framework.