Conformal quantum effects and the anisotropic singularities of scalar-tensor theories of gravity

TL;DR

This paper demonstrates that adding a conformal Weyl tensor squared term to scalar-tensor gravity actions can eliminate anisotropic singularities, preserving isotropic solutions and potentially arising from quantum considerations, thus revitalizing certain scalar field models.

Contribution

It introduces a higher-order curvature term to scalar-tensor theories to remove anisotropic singularities while maintaining isotropic solutions, linking quantum effects to classical gravity modifications.

Findings

The $C_{abcd}C^{abcd}$ term removes anisotropic singularities.

Isotropic solutions are preserved despite the added term.

The approach revitalizes scalar field models previously dismissed due to anisotropic instabilities.

Abstract

We show that the inclusion of a term $C_{abcd}C^{abcd}$ in the action can remove the recently described anisotropic singularity occurring on the hypersurface $F(\phi)=0$ of scalar-tensor theories of gravity of the type $$ S=\int d^4x \sqrt{-g} {F(\phi)R - \partial_a\phi\partial^a\phi -2V(\phi)}, $$ 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 ($F(\phi)=1-{1/6}\phi^2$) with potential $V(\phi)=\frac{m}{2}\phi^2 -\frac{\Omega}{4}\phi^4$, that have been discharged as unrealistic precisely by their anisotropic instabilities on the hypersurface $F(\phi)=0$.