Scalar domain wall as the universe

Abstract

We develop a formulation where, for an arbitrarily given warp factor, we construct a scalar field action which reproduces the warp factor as a solution of the Einstein equation and field equation corresponding to the action. This formulation could be called the reconstruction. By using the formulation of the reconstruction, we construct models which have an exact solution describing the domain wall. The shape of the domain wall can be flat, de Sitter space-time, or anti-de Sitter space-time. In the constructed domain wall solutions, there often appears a ghost with negative kinetic energy. We give, however, an example of the de Sitter domain wall solution without a ghost, which could be a toy model of inflation. We also investigate the localization of gravity as in the Randall-Sundrum model. It is demonstrated that the four-dimensional Newton law could be reproduced even in the de Sitter space-time domain wall solution. We show that we can construct a space-time, where the domain wall is the general Friedmann-Robertson-Walker universe and the warp factor can be arbitrary. For such a construction, we use two scalar fields. It is also illustrated that the scalar field equations are equivalent to the Bianchi identities: ${\ensuremath{\nabla}}^{\ensuremath{\mu}}({R}_{\ensuremath{\mu}\ensuremath{\nu}}\ensuremath{-}\frac{1}{2}R{g}_{\ensuremath{\mu}\ensuremath{\nu}})=0$.