No abstract

It is shown that the effective five-dimensional theory of the strongly coupled heterotic string is a gauged version of Nϭ1 five-dimensional supergravity with four-dimensional boundaries. For the universal supermultiplets, this theory is explicitly constructed by a generalized dimensional reduction procedure on a Calabi-Yau manifold. A crucial ingredient in the reduction is the retention of a ''non-zero mode'' of the four-form field strength, leading to the gauging of the universal hypermultiplet by the graviphoton. We show that this theory has an exact three-brane domain wall solution which reduces to Witten's ''deformed'' Calabi-Yau background upon linearization. This solution consists of two parallel three-branes with sources provided by the fourdimensional boundary theories and constitutes the appropriate background for a reduction to four dimensions. Four-dimensional space-time is then identified with the three-brane world volume. ͓S0556-2821͑98͒02122-5͔

We consider conditions under which a universe contracting towards a big crunch can make a transition to an expanding big bang universe. A promising example is 11-dimensional M-theory in which the eleventh dimension collapses, bounces, and re-expands. At the bounce, the model can reduce to a weakly coupled heterotic string theory and, we conjecture, it may be possible to follow the transition from contraction to expansion. The possibility opens the door to new classes of cosmological models. For example, we discuss how it suggests a major simplification and modification of the recently proposed ekpyrotic scenario.

We study the generation of density perturbations in the ekpyrotic scenario for the early universe, including gravitational backreaction. We expose interesting subtleties that apply to both inflationary and ekpyrotic models. Our analysis includes a detailed proposal of how the perturbations generated in a contracting phase may be matched across a 'bounce' to those in an expanding hot big bang phase. For the physical conditions relevant to the ekpyrotic scenario, we re-obtain our earlier result of a nearly scale-invariant spectrum of energy density perturbations. We find that the perturbation amplitude is typically small, as desired to match observation. Typeset using REVT E X 1We recently proposed a novel scenario for the early Universe in which the hot big bang is created by the collision between two M-theory branes 1 . The scenario assumes the Universe begins in an almost static, nearly BPS initial state consisting of empty, flat, parallel threebranes. In the effective 4d theory, the BPS state is homogeneous and has zero spatial curvature. Due to non-perturbative effects, however, a tiny force attracts the branes to one another. As the branes come together, quantum fluctuations create ripples in the brane surfaces that result in spatial variations in the time of collision. Consequently, some regions heat up and begin to cool before others, producing a spectrum of long wavelength density perturbations which can seed structure formation in the Universe.We estimated the perturbation spectrum using a 'time delay' formalism 2 , often used in simplified treatments of inflationary models. In that context, spatial variations in the time when inflation ends result in long wavelength density inhomogeneities. We applied the same formalism to variations in the time of collision in the ekpyrotic scenario. The equation for fluctuations in the scalar field φ describing the inter-brane separation in the ekpyrotic model is almost identical to that describing fluctuations in the inflaton during slow-roll inflation. Consequently, a nearly scale-invariant spectrum of fluctuations is found.The result is remarkable because it shows that the Harrison-Zel'dovich spectrum can be obtained without inflation in a space-time which is very nearly static Minkowski space.The time delay formalism is a crude approximation, and only quantitatively accurate for a small class of inflationary potentials 3 . Nevertheless, it often gives a good estimate of the spectral index for the power spectrum of perturbations. One of the goals of this paper is to investigate whether the same statement is true for the ekpyrotic model.In the case of the ekpyrotic model, there is the major complication that the perturbations are produced when the effective 4d scale factor is contracting. In order to have a viable scenario, a mechanism must be found to reverse from contraction to expansion. This issue has been addressed in a recent paper we have written with N. Seiberg 4 , where we argue that such a 'bounce' may be allowed in the context of M-theory, where i...

Inflationary solutions are constructed in a specific five-dimensional model with boundaries motivated by heterotic M theory. We concentrate on the case where the vacuum energy is provided by potentials on those boundaries. It is pointed out that the presence of such potentials necessarily excites bulk fields. We distinguish a linear and a non-linear regime for those modes. In the linear regime, inflation can be discussed in an effective four-dimensional theory in the conventional way. This effective action is derived by integrating out the bulk modes. Therefore, these modes do not give rise to excited Kaluza-Klein modes from a four-dimensional perspective. We lift a four-dimensional inflating solution up to five dimensions where it represents an inflating domain wall pair. This shows explicitly the inhomogeneity in the fifth dimension. We also demonstrate the existence of inflating solutions with unconventional properties in the non-linear regime. Specifically, we find solutions with and without an horizon between the two boundaries. These solutions have certain problems associated with the stability of the additional dimension and the persistence of initial excitations of the Kaluza-Klein modes.