We provide a simple macroscopic analysis of the four-dimensional effective supergravity of the Hořava-Witten M -theory which is expanded in powers of κ 2/3 /ρV 1/3 and κ 2/3 ρ/V 2/3 where κ 2 , V and ρ denote the eleven-dimensional gravitational coupling, the Calabi-Yau volume and the eleventh length respectively. Possible higher order terms in the Kähler potential are identified and matched with the heterotic string corrections. In the context of this Mtheory expansion, we analyze the soft supersymmetry-breaking terms under the assumption that supersymmetry is spontaneously broken by the auxiliary components of the bulk moduli superfields. It is examined how the pattern of soft terms changes when one moves from the weakly coupled heterotic string limit to the M -theory limit.

We study the cosmological gravitino production in gauge mediated supersymmetry breaking models, while properly taking into account the existence of the messenger mass scale. It is found that for sizable parameter range of the model the messenger sector contribution leads to more stringent upper bound on the reheat temperature obtained from the condition that the universe should not be overclosed by relic gravitinos. However it turns out that in the limit of relatively low messenger scale and large gravitino mass, the relic gravitino mass density can be smaller than the critical density independently of the reheat temperature, suggesting the possibility in this limit to have a high reheat temperature without the dilution of gravitinos at late time.

We examine the stabilization of the two typical moduli, the length ρ of the eleventh segment and the volume V of the internal six manifold, in compactified heterotic M -theory. It is shown that, under certain conditions, the phenomenologically favored vacuum expectation values of ρ and V can be obtained by the combined effects of multi-gaugino condensations on the hidden wall and the membrane instantons wrapping the three cycle of the internal six manifold.