On the singularities of gravity in the presence of non-minimally coupled scalar fields

We investigate the robustness of some recent results obtained for homogeneous and isotropic cosmological models with conformally coupled scalar fields. For this purpose, we investigate anisotropic homogeneous solutions of the models described by the action $$S=\int d^{4}x\sqrt{-g}\{F(\varphi )R-{\mathrm{\partial }}_a\varphi {\mathrm{\partial }}^a\varphi -2V(\varphi )\},$$ with general $F(\varphi )$ and $V(\varphi )$. We show that such a class of models leads generically to geometrical singularities if for some value of $\varphi$, $F(\varphi )=0$, rendering previous cosmological results obtained for the conformal coupling case highly unstable. We show that stable models can be obtained for suitable choices of $F(\varphi )$ and $V(\varphi )$. Implications for other recent results are also discussed.