  We discuss theories in which the standard-model particles are localized on a
brane embedded in space-time with large compact extra dimensions, whereas
gravity propagates in the bulk. In addition to the ground state corresponding
to a straight infinite brane, such theories admit a (one parameter) family of
stable configurations corresponding to branes wrapping with certain periodicity
around the extra dimension(s) when one moves along a noncompact coordinate
(tilted walls). In the effective four-dimensional field-theory picture, such
walls are interpreted as one of the (stable) solutions with the constant
gradient energy, discussed earlier. In the cosmological context their energy
"redshifts" by the Hubble expansion and dissipates slower then the one in
matter or radiation. The tilted wall eventually starts to dominate the
Universe. The upper bound on the energy density coincides with the present
critical energy density. Thus, this mechanism can become significant any time
in the future. The solutions we discuss are characterized by a tiny spontaneous
breaking of both the Lorentz and rotational invariances. Small calculable
Lorentz noninvariant terms in the standard-model Lagrangian are induced. Thus,
the tilted walls provide a framework for the spontaneous breaking of the
Lorentz invariance.
