The Hierarchy Problem and $\mathcal{N} =2$ $\mathcal{D} = 5$ Supergravity

We introduce a new scenario to solve the hierarchy problem based on $\mathcal{N}=2$, five-dimensional supergravity compactified on Calabi-Yau threefold down from $\mathcal{D}=11$ supergravity. When modeling the universe as a 3-brane embedded in a five-dimensional bulk, the background metric is proportional to one of the hypermultiplets fields, namely the dilaton, the volume modulus of the Calabi-Yau space. When solving the dilaton field equation, we find that it is dependent on the extra dimension. We solve the modified Friedmann equations and find the implications of the model on the relation between the effective four-dimensional gravity scale in the brane and the Planck scale of the fifth extra dimension ($\mathcal{M}$). A couple of different scales are considered for the extra dimension, the first where the extra dimension is in range of the solar system and $\mathcal{M}$ is of order of the electroweak scale, and the second where the scale of the extra dimension is of order $\mu m$ and the higher dimensional Planck scale $\mathcal{M} \sim 10^{13} ~ \text{GeV}$. In both cases, the signatures of Kaluza-Klein excitations are quite distinct from the signatures of any previous extra dimensions model.