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When N= D=11 supergravity is compactified on CY threefold to N=2 D=5 supergravity the action of the last is given in terms of the geometery of the CY manifold space, namely, in terms of the hypermultiplets. There are $z^i(i=1,...,h^{2,1})$ complex structure moduli in the moduli space of the CY manifold which is a special K\"ahler manifold with a metric $G_{i\bar{j}}$. We solve the field equations of the complex structure moduli with the solution of the Einstein field equations to the moduli velocity norm $G_{i\bar{j}} z^i z^{\bar{j}}$ in case of a 3- brane filled with radiation, dust and energy embedded in the bulk of D=5 supergravity. We get the time dependence of the moduli and the metric. Then we can further deduce the geometry of the moduli space by getting the K\"ahler potential which directly relates to the volume of the CY manifold., Comment: 13 pages, 7 figures

In this paper we extend previous work on the relation between the complex structure moduli of the underlying Calabi-Yau manifold in five dimensional supergravity with the time evolution of an embedded 3-brane. We numerically solve the fields' equations for such a construction and focus on dust and radiation filled branes; with the possible application of modeling the universe as a brane-world. It is shown that in both cases the time evolution of the moduli causally connects to the expansion of the brane-world. We also find that in most cases considered there is an early short period of rapid accelerative expansion, indicating an inflationary epoch. We report on these results; leaving analysis of the underlying causes for future work., Comment: 22 pages, 14 figures. Class. Quantum Grav. (2020)