Attractor in a superstring model: The Einstein theory, the Friedmann universe, and inflation

In a superstring model, the minimum of the supersymmetry-breaking potential through a gluino condensation provides a no-scale model, which may explain the hierarchy problem, permit inflation, and give zero cosmological constant naturally. It is shown that the above minimum is an attractor in the dynamical system. This minimum also guarantees the four-dimensional Einstein gravity theory, rather than the Brans-Dicke theory, in the low-energy limit. Using this model a preferential scenario of evolution toward (the four-dimensional Friedmann universe)×(a static Calabi-Yau space) via inflation is discussed. A series of phase transitions due to a quantum tunneling of the quantized antisymmetric field H may occur, forming a hierarchical bubble structure.