Tilting the Brane, or Some Cosmological Consequences of the Brane Universe

TL;DR

This paper explores how tilted brane configurations in extra-dimensional theories can influence cosmology by acting as a slowly redshifting energy component, potentially dominating the universe's energy density in the future, and inducing spontaneous Lorentz symmetry breaking.

Contribution

It introduces stable tilted brane solutions in extra-dimensional models and analyzes their cosmological impact and implications for Lorentz symmetry breaking.

Findings

Tilted branes can dominate the universe's energy density in the future.

These configurations induce small Lorentz noninvariant terms in the standard model.

The energy density of tilted walls redshifts slower than matter or radiation.

Abstract

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.