Eur. Phys. J. C 25, 157-164 (2002)
Cosmological evolution in compactified Horava-Witten theory induced by matter on the branesU. Ellwanger
Laboratoire de Physique Théorique (Unité Mixte de Recherche - CNRS - UMR 8627) , Université de Paris XI, Bâtiment 210, 91405 Orsay Cedex, France
(Received: 8 April 2002 / Published online: 26 July 2002 )
The combined Einstein equations and scalar equation of motion in the Horava-Witten scenario of the strongly coupled heterotic string compactified on a Calabi-Yau manifold are solved in the presence of additional matter densities on the branes. We take into account the universal Calabi-Yau modulus with potentials in the 5- d bulk and on the 3-branes, and allow for an arbitrary coupling of the additional matter to and an arbitrary equation of state. No ad hoc stabilization of the five dimensional radius is assumed. The matter densities are assumed to be small compared to the potential for on the branes; in this approximation we find solutions in the bulk which are exact in y and t. Depending on the coupling of the matter to and its equation of state, various solutions for the metric on the branes and in the 5- d bulk are obtained: solutions corresponding to a "rolling radius", and solutions with a static 5- d radius, which reproduce the standard cosmological evolution.
© Società Italiana di Fisica, Springer-Verlag 2002