Brans-Dicke supergravity and the Lambda naturalness problem

The successful $\Lambda CDM$ cosmological model requires a small but nonzero $\Lambda$ which appears to have an unnaturally small value compared to the supersymmetry breaking scale, typically $O(10^{-60}) m_{3/2}^4$ for $m_{3/2} \sim 10 TeV$. We explore the possibility of solving this naturalness problem in a special class of no-scale supergravity models which arise from a supersymmetric version of Brans-Dicke gravity, in which the Volkov and Brans-Dicke multiplets may be identified. These may be embedded in compactified string models, with the Brans-Dicke scalar given by the combination of dilaton and compactification breathing modes which leaves the 4 dimensional gauge couplings fixed. Assuming that 4 dimensional physics has an approximate symmetry under changes in this mode broken only by couplings between the low energy and gravitational or string sectors, the main one loop contribution to $\Lambda$ cancels between Brans-Dicke and gravitational (conformal compensator) F terms, and the leading contributions to $\Lambda$ now appear to be $O(m_{3/2}^8 m_{p}^{-4)}$, enabling a natural reconciliation between observational and particle physics estimates for $\Lambda$.
The Brans-Dicke scalar has a range $O(m_{3/2}^{-1})$, lifting observational constraints on scalar gravity in this scenario.