Conformal Quantum Effects and the Anisotropic Singularities of Scalar-Tensor Theories of Gravity

We show that the inclusion of a term CabcdCabcd in the action can remove the recently described anisotropic singularity occurring on the hypersurface F (φ) = 0 of scalar-tensor theories of gravity of the type \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$S = \int {d^4 x\sqrt { - g} \{ F(\phi )R - \partial _a \phi } \partial ^a \phi - 2V(\phi )\} ,$$ \end{document} preserving, by construction, all of their isotropic solutions. We show that, in principle, a higher order term of this type can arise from considerations about the renormalizability of the semiclassical approach to the theory. Such result brings again into consideration the quintessential models recently proposed based in a conformally coupled scalar field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$(F(\phi ^2 ) = 1 - \frac{1}{6}\phi ^2 )$$ \end{document} with potential \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$V(\phi ) = \frac{m}{2}\phi ^2 - \frac{\Omega }{4}\phi ^4 $$ \end{document}, that have been discharged as unrealistic precisely by their anisotropic instabilities on the hypersurface F (φ) = 0.